Systems of linear inequalities word problems worksheet pdf

Constraining solutions of systems of inequalities. 905 ≤ 500 + 15h 905 ≤ 500 + 15(27) 905 ≤ 905 Step 7. How The worksheets on this page require kids to solve inequalities by graphing. 22) Name one particular solution to question #20. 1. 5 liters of shampoo. 14. And the graph of linear inequality is the graph for all Try it! Try: write a system of linear inequalities. x < - 3 divide both sides by 3. 6 ounces of the 10 % solution. A jar containing only nickels and dimes contains a total of 60 coins. Worksheet by Kuta Software LLC. Oct 6, 2021 · Solution: Begin by solving both inequalities for y. Therefore, our system of linear equations is: 50x+45y≥500 x+y=20. Fancy shirts cost $28 and plain shirts cost $15. In the example above x < 2 is the solution. Sheet 2 involves the same skills as Sheet 1 but has compound inequalities in each question. ** THE FLIPPER RULE . Word Problems Worksheet 1 – This 6 problem algebra worksheet will help you practice solving real-life systems of equations problems using the “ substitution ” method. Graph the solution on a number line. Observe whether it makes the actual inequality true or not. Use a dashed line for each boundary. Altogether these animals have 60 legs. Keywords/Tags: word problems, applications, real-life, linear Regents-Modeling Linear Systems 3 A/B: 26/3: TST PDF DOC: Regents-Modeling Linear Systems 4 AL: 12: TST PDF DOC: Regents-Modeling Systems of Linear Inequalities AI/AI: 1/9: TST PDF DOC: Practice-Modeling Linear Systems 1 ratio: 10: WS PDF: Practice-Modeling Linear Systems 2 mixed: 17: WS PDF: Practice-Modeling Linear Systems 3 break even: 10 Two-variable inequalities word problems. A warehouse worker uses a forklift to move boxes that weigh either 45 pounds or 70 pounds each. All of the coefficients and answers are positive integers. $14. Unit 5: Radicals. by Thomas Hyun. 4 and 8 2) The difference of two numbers is 3. Guidelines for translating word problems into inequalities: 1. A. Even though 9 is not a solution, it is a crucial value or point of division that is vital to explore the solution. Always put related numbers in the same inequality. Regents Exam Questions A. Check the answer in the problem and make sure it makes sense. Recommendations. 50x+45y≥500 is represented by the red shading. org 1 A. It is the solution to all inequalities in the system. com. The worksheet attached below will provide you with some practice using number lines to communicate your answers to inequality word problems. Solve each system by elimination. 3 2. The quiz will have 15 questions with field’s dimensions. • Numbers can be related by being in the same sentence or having the same symbols Mar 18, 2024 · Worksheet inequalities worksheets graphing linear solving equations algebra systems inequality answers functions system pdf worksheeto line number via chessmuseum 2021Solving linear inequalities worksheet for 10th grade Inequalities linear solving worksheet grade lessonSolving linear inequalities hangman worksheet answer key 2010 worksheet. 1. ( − 3, 3) is not a solution; it does not satisfy both inequalities. W. 30 nickels and 30 dimes. C. Example 1: A farmhouse shelters 16 animals. Some are chickens and some are pigs. Math is FUNtastic. Description: Solve word problems leading to inequalities of the form px + q > r or px + q r, where p, q, and r are specific rational numbers. (Opens a modal) Systems of equations with elimination: potato chips. Slope-intercept form is best way to identify the slope of the line and the y-intercept of the line. Linear Inequalities A linear inequality in two variables, x and y, can be written as ax + by < c ax + by ≤ c ax + by > c ax + by ≥ c where a, b, and c are real numbers. These are 9 of my favorite joke worksheets to use in my Systems of Equations/ Inequalities Unit in Algebra 2. Dec 31, 2023 · Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Probability using permutations and combinations. Ex: 2 x ≥ x + 2. a) Choose a variable and write an inequality for this problem. Writing Numbers in Scientific Notation. Graph y < x and x > 5 on the axes below. View more like this: Algebra 1, Algebra 1 Units. (Opens a modal) Systems of equations with elimination (and manipulation) (Opens a modal) Elimination method review (systems of linear equations) (Opens a modal) • illustrate linear inequalities in two variables; • graph linear inequalities in two variables on the coordinate plane; and • solve real-life problems involving linear inequalities in two variables. 3x - 7 > 20 Step 1: 3 (10) - 7 > 20 Step 2: 30 - 7 > 20 Step 3 Aug 24, 2020 · To solve a system of linear inequalities, we will find values of the variables that are solutions to both inequalities. Microsoft Word - DLASystemWordProblems. comLinear equation word problems worksheet homeschooldressage. Made using Desmos. For the first inequality, shade all points above the boundary. Triniti had $500 in a saving account at the beginning of the summer. 20 + 6= D. Linear Inequalities in Two Variables Create your own worksheets like this one with Infinite Algebra 1. For example, both solution sets of the following inequalities can be graphed on the same set of axes: {y < 1 2x + 4 y ≥ x2. Write an inequality to represent this situation. Type 3: Solve the given (very simple) inequality in the given set. Combinations. . Work with a partner. Unit 4: Inequalities. 9 Try This: Example 3 Continued The length of the envelope must be between Apr 5, 2024 · There are a few ways that we can write linear equations, with two of the most common being slope-intercept form and standard form. ,wehavealinear inequality. Skill plans. Writing linear equations. Awards. Solving linear inequalities is very much the same as solving linear equations with one very important exception! Dec 27, 2023 · Systems of inequalities: word problemsSystem of inequalities worksheet : systems of inequalities practice Equations linear solving variables algebra inequalities elimination writing given purplemath algebraic points2021 system of inequalities worksheet pdf / cool math 24 abacus. Finding slope from two points. Acing the New SAT Math. Figure 3. Tackle this batch of printable inequalities worksheets by plugging each of the four options in the inequality statement. How many people could attend the function if they rented the banquet hall? a) Choose a variable and write an Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. 3x < - 9 add 5 to both sides. She has to first buy the fruit from the grocery store and pays $2 per apple and $3 per orange and only has $18 to spend. Customers can buy apple pies and lemon meringue pies. So, we can say that: x+y=20. Wang Hao wants to spend at most $ 15 on dairy products. Problems word inequality worksheet math inequalities worksheets grade 7th solving 8th chessmuseum equations problem applying linear choose Algebra 1 – Spencer – Unit 4 Notes: Inequalities and Graphing Linear Equations ** Multiplication and Division Properties of Equality introduce a new concept. Some of the questions ask you to find the inequality variables’ values. Graphing Systems of Linear Inequalities in Two Variables To graph a system of linear inequalities in two variables, we want to find every possible Apr 7, 2024 · Writing linear equations from word problems worksheet pdf — db-excel. G. B. Then we subtract x: 16 = 2x. Systems of Equations Word Problems Date_____ Period____ 1) Kristin spent $131 on shirts. k e IM9aUdceY HwOiht fh s DIEnZfiBnnintrev lP 0rner-eA ylLguedbkr 1aX. Two Step Inequalities. Each liter of goat milk costs $ 2. One Step Inequalities. 2 Systems of Linear Equations in Two Variables ©C F2M0T2^0J fKiuOt]aH ySAoNfhtXwpaZr_eX mLELSCX. We solve the system by using the graphs of each inequality and show the solution as a graph. translate statements into mathematical expressions. Complete answers and explanations help you identify weaknesses and attain maximum benefits out of the practice test. Understand the Problem Try This: Example 3 Continued Show the relationship of the information: 1 . Essential Question How can you graph a linear inequality in two variables? A solution of a linear inequality in two variables is an ordered pair (x, y) that makes the inequality true. The cost to rent a banquet hall is $500, plus $35 per person. Graphing lines using standard form. 25) Write a system of equations with the solution. 3) Castel and Gabriella are selling pies for a school fundraiser. 80 plus $0. Permutations. So, when you multiply or divide both sides by a negative number, just flip the inequality!! Watch: −3x > 15 Systems of Linear Inequalities Word Problems Puzzle. Worksheet by Kuta Software LLC 7. Solution. This is an involved concept and typically difficult for many Algebra students. Choose AT LEAST one type. Any number greater than zero. 7. Here is a graph of the two inequalities. Their sum is 13. a. Word Problems Worksheet 1 – This 6 problem algebra worksheet will help you practice creating and solving systems of equations to represent real-life situations. Country code: US. Step 2: Solve the inequalities. Students will need to cut out 18 puzzle pieces and match them together in groups of four ( word problem, defined variables, inequalities, and graph). We substitute 27 into the inequality. b) Solve the inequality. 250x + 500y > 2000 (Red Line) x-int: (8,0) Y int: (0, 4) Systems of inequalities word problems. 8. A large pizza at Palanzio’s Pizzeria costs $6. Learn for free about math, art Jan 21, 2024 · Step 5. sal shades the overlap due to the property of inequalitites. The graph of a linear inequality in two variables shows all the solutions of the inequality in a coordinate plane. This puzzle includes 6 questions that are designed to help students practice solving real-life systems of inequalities. If she bought a total of 7 then how many of each kind did she buy? 2 fancy shirts and 5 plain shirts 2) There are 13 animals in the barn. by. ©l R2J0 G1c2x sK vu Xt1a9 MS9o hf AtMwNaHr5e W 1L vLYCe. Solution: Adding 9 to a number is written as x + 9, while subtracting 7 from three times the number is written as 3x − 7. For the second inequality, shade all points below the boundary. Write an equation Original equation: 5F + 3B = D, F=4 and B=2. 45. There is a maximum of 800 tickets for the show. Some of them are chickens and the others are cows. To solve an inequality word problem, we must translate the numbers in the problem into inequalities, and graph the inequality on the coordinate plane. 4. When multiplying . 5 A high school drama club is putting on their annual theater production. The value of all the coins in the jar is $4. Graphing linear inequalities. Step 1: Graph the boundary line. How many downloads can Kevin purchase? Justify your answer. Your teacher announced a 50 point math quiz The length is 12ft longer than the width. The costs of the tickets are $6 before the day of the show and $9 on the day of the show. Grade 6 students circle all the possible values that make the inequality statement true. jmap. Mutualy exclusive events. Show all the possible combinations of fruit she can sell. x + y = 8 4. com 1. doc. u O JA[lhlD HryiTg]hVt]sm ArheJsIeuryv[egdK. 6) Alberto and Aliyah are selling fruit for a school fundraiser. Improve your math knowledge with free questions in "Write two-variable inequalities: word problems" and thousands of other math skills. To meet the expenses of the show, the club must sell at least $5,000 worth of tickets. This algebra 2 systems of inequalities worksheet will produce eight problems per page. Many answers. Inequality Word Problems Worksheet Algebra 1 Answers — db-excel. com Create your own worksheets like this one with Infinite Algebra 1. linear inequality in two variables, p. PDF. Download the set. In general, the equation of a line in slope-intercept form is written as: y = ax + b. A system of linear inequalities in two variables refers to or consists of at least two inequalities in the same variable. The best way to get a grip around these kinds of word problems is through practice, so we will solve a few examples here to get you accustomed to finding elements of linear systems inside of word problems. Students will need to cut out 18 puzzle pieces and match them together in groups of four (word problem, defined variables This point does satisfy the inequality. Ex: x + y = 1, 2 x + y = 5. On the set of axes below, solve the following system of inequalities graphically. Jeopardy Review Game: Systems of Equations Size of the graph images (in pixels): Choose the types of problems for the worksheet. (2 points) In order to graph, we will first find the x-intercepts of both equations because we must determine the scale that will be used on the x and y axis. Write an inequality that represents the number of liters of goat milk ( G) and cow's milk ( C) Wang Hao can buy on his budget. x+y=20 is represented by the blue shading. x > 0, y > 0-3-Create your own worksheets like this one with Infinite Algebra 2. Step 2: Test a point not on the boundary. Step 2 Add or subtract the equations to eliminate one of the variables. Learn Problem Solving Techniques. A solution of a linear inequality in two variables is an ordered pair (x, y) that makes the inequality true. Finding slope from an equation. You may select which type of method the student should use to solve the problems. There are 40 legs in all. L Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Systems of Equations Word Problems Date_____ Period____ 1) Find the value of two numbers if their sum is 12 and their difference is 4. Flying into the same wind the plane only went 141 km/h. Alberto sold 12 small boxes of tangerines and 6 large boxes of tangerines for a total of $330. Algebra 1 notes and in class practice over Systems of Linear Inequalities Word Problems. Solving a Linear Inequality Word Problem Example. x > 50. Solving Systems of Equations by Graphing2. Solving systems of equations word problems worksheet For all problems, define variables, write the system of equations and solve for all variables. Solve by the method of your choice. Step 1 Multiply, if necessary, one or both equations by a constant so at least one pair of like terms has the same or opposite coefi cients. Write an inequality that represents Kevin’s situation. Ex: 4. Members of the swim team want to wash their hair. Word-Problems-System-of-Linear-Equation-in-Two-Variables. 6. Test prep. Systems of equations with elimination: x-4y=-18 & -x+3y=11. By inspection, we see that the slope is m = − 3 = − 3 1 = rise run and the y -intercept is (0, 1). Find the for tomorrow. the number of hours Brenda must babysit Let h = the number of hours. 3 2 5 length width Make a Plan You can use the model from the previous slide to write an inequality where l is the length and 4. After dividing by 2, we obtain the answer x = 8. Graphing absolute value equations. Sample spaces and The Counting Principle. Worksheet includes graphs for students to graph on as well. 3x - 7 = 20 Step 1: 3 (9) - 7 = 20 Step 2: 27 - 7 = 20. Convert it to a fraction over 1 or an improper fraction if it is not already in Writing Inequalities from Word Problems - Section C. Title: Word Problems Involving Linear Systems in Two Variables Class: Math 100 or Math 107 Author: Sharareh Masooman Instructions to tutor: Read instructions under “Activity” and follow all steps for each problem exactly as given. ≥ − 1. 11) The school that Darryl goes to is selling tickets to a choral performance. 13) State one solution to the system y < 2x − 1 y ≥ 10 − x Many solutions. 2 Graph the boundary line between two half planes for each inequality in a system of linear inequalities, and justify the choice of solid or broken lines. K. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. 0 Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Inequalities and Their Graphs Date_____ Period____ This activity allows students to create systems of linear inequalities from word problems, create a graph to model their system, and answer questions involving their system of linear inequalities. Graph both inequalities in the same coordinate y plane. Subjects: Algebra 2. Graph the solution set of the inequality and interpret it in the context of the problem. to help remember how to graph these inequalities, remember: Solving a System of Linear Equations by Elimination. The forklift can carry up to either 60 boxes or a weight of 3000 pounds. Find the numbers. Together she can sell a maximum of 12 pieces of fruit. Step 3 Solve the resulting equation. d R OAYlMl0 5rDiRguhbtAsX SrReBsweUr3voeRdK. Apr 17, 2020 · 17/04/2020. Free Algebra 2 worksheets created with Infinite Algebra 2. 1 Model a problem, using a system of linear inequalities in two variables. Solve the inequality. 5 (4) + 3 (2) = D. More Radicals Worksheets Compound Inequalities Worksheets Graphing Inequalities Worksheets Inequality Word Problems Worksheets Systems of Inequalities Worksheets Solving Equations and Inequalities Worksheets Only a nontransferable license is available for this resource. The school took in $105 on the second day by selling 3 adult tickets and 12 student tickets. You will use the “ elimination ” method to eliminate variables from standard form equations. Customers can buy small boxes of tangerines and large boxes of tangerines. All five problems feature a vertical line from an inequality that acts as the domain, such as w > 5. Graphing Inequalities. Free trial available at KutaSoftware. Grades: The worksheets given here require students to solve inequalities in the regular way and also on the number line. This algebra 2 systems of inequalities worksheet will produce problems for solving two variable systems of inequalities graphically. x + 4. Description. Independent and dependent events. 5 l 4. • Graph the system of inequalities on the grid. We therefore get the equation: x + 9 = 3x − 7. Direct variation. We will find the region on the plane that contains all ordered pairs (x, y) that make both inequalities true. Lesson 1- Solving Problems Involving Linear Inequalities in Two Variables. b A 6A MlPlk LrXiCg dhPtdsw Mrle EsRejr ovQeMdf. 1 we studied linear equations that can be written in the form ax 1 by 5 c. Virginia state standards. Answer the the question with a complete sentence. 5. 00 ISBN 978-0-9754753-6-2PDF. Linear inequalities is a part of syllabus in algebra 1 (second math course), which finds application in many algebra questions including algebra word problems. Create your own worksheets like this one with Infinite Algebra 2. 3. IXL plans. Solving Systems of Equations Using Substitution Day 13. Step 4: Shade in the half-plane to the right of the line. Let's solve these inequalities by graphing. The solution to this inequality is all real numbers less than -3. Word Problems Worksheet 1 PDF. If you have a linear inequality in slope intercept form, you can use these steps to graph that inequality on the coordinate plane: Plot the y-intercept point on the coordinate plane at the (0,b) point. 23. The graph of the system is the intersection of the two half-planes, which is the region shown in the darker shade of blue. 7: Systems of Linear Inequalities: Graph and solve systems of linear equations and inequalities with rational coefficients in two variables. -1-To use the method of elimination to solve a system of two linear equations in x and y, perform the following steps. Age problems are common applications that you will see when solving linear inequality word problems. 70 L + 60 S < 5600 represents the number of long-haired members L and short-haired members S who can wash their hair with less than 5600 liters of water. Here's how I came up with this inequality. We obtain the following equivalent system: Add the equations and then solve for x: Back substitute. She wants to have at least $200 in the account by the end of the summer. 26=D. Choose a point in the dark blue region, such as (0, 1). 20 . Module MapModule Map This chart shows the lessons that will be covered in this module. Find the speed of the plane in still air and the speed of the wind. 26=30 is not correct, and so does not satisfy the inequality. While the inequalities are directly given in some worksheets, some have word problems that require you to frame them. The example that follows illustrates a technique for representing the solution set for a linear inequality. Multi-Step Inequalities (#1-10 are variables on one side, #11-24 have variables on both sides) Compound Inequalities. In this case, graph a dashed line y = − 3x + 1 because of the strict inequality. State the coordinates of a point in the solution set. A. Aug 25, 2023 · Linear equations word problems grade 9 pdfEquations solving algebra key soe inequalities Word equations problems linear systems writing solving math algebra solve preview pdf corse badminton. Then, we will select the value greater than 9 to 10. < 2x + 1. 2x+5 < 9 is an example of linear inequalities in one variable. The bathroom has less than 5600 liters of water and at most 2. Figure 4. 4 = 8− 4. ©B U2l0H1e2M pKtultjaf QSNo5fvt6wsawroem gL4LjCU. Micah. Graphing linear inequalities and systems of inequalities. 4+ y = 8 4. "Go To" games, the M and M activity, and the real-world Burgers activity! Systems Unit Notes for ActivInspire (Promethean Board) Systems of Inequalities - Real World Word Problems. Country: United States. Systems of Linear Inequalities Word Problems Puzzle. Word Problems Worksheet 1 RTF. 2x + 3y > 500. 9. 4. Then list two possible combinations. Therefore, every point in the half-plane to the right of the line satisfies the inequality. Step 6. 9 is the height. This document contains 3 pages: one for a teacher model, one for Linear Inequalities In Section 9. Solving Systems of Equations Using Substitution Day 24. 90 for each topping. Oct 13, 2023 · Equations algebra systems solving problems3 variable system of equations word problems worksheet pdf Understanding and solving one-variable equationsQuiz & worksheet. Worksheet by Kuta Software LLC-2-Solve each word problem by writing and solving a system of equations. Textbooks. xps. Ex: (10 , 10) or (5, 8) 14) Write a system of inequalities whose solution is the set of all points in quadrant I not including the axes. com Solving systems of equations word problems worksheet worksheet : resume. 40: Systems of Linear Inequalities: Determine whether a given point is in the solution set of a system of linear inequalities 1 Which ordered pair is in the solution set of the following system of inequalities? 1) 2) 3) 4) This topic covers: Solutions to linear inequalities and systems of inequalities. 29 nickels and 31 dimes. A company’s social committee has $4700 to put towards renting a banquet hall. apply linear inequalities in two variables in real-life situation. Example 1. Graphing Linear Equations Word Problems Worksheet Answers Pdf Word Problems. However we already know that D is actually equal to 30 using the graph so. Type 1: Plot a given inequality on a number line (such as plot x ≤ −5) Type 2: Write an inequality that corresponds to the plot on the number line. After going through this module, you are expected to: 1. Solve by elimination to find the number of nickels and dimes that are in the jar. Sheet 1 involves using one variables and using the information to solve the inequality, usually in the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. 5 years ago. 40: Systems of Linear Inequalities Name: _____ www. The directions are from TAKS so do all three (variables, equations and solve) no matter what is asked in the problem. 3 Determine and explain the solution region that satisfies a linear inequality, using a test point when given Oct 6, 2021 · Answer. Graphing Inequalities on a Number Line. Testing solutions to systems of inequalities. School subject: Math (1061955) Main content: Inequalities (2010793) From worksheet author: Word Problems with inequalities. Solve 3x – 5 < –14. This can be used as an introduction to systems of linear inequalities by graphing. 4 ounces of the 50 % alcohol solution and 3. Set up a system of equations needed to solve each problem. 13. This unit includes 64 pages of guided notes, homework assignments, three quizzes, a study guide, and a unit test that cover the topics listed in the description below. She withdraws $25 each week for food, Apr 1, 2024 · 29 inequality word problems worksheet algebra 1Inequalities systems problems word problem answer practice algebra system solution depending ordered pairs vary final which may Graphing systems of inequalities from a word problem worksheet byInequality algebra checking. Let x be the number of 45 -pound boxes and y be the number of 70 -pound boxes. Printable in convenient PDF format. (71) $2. 40 , and each liter of cow's milk costs $ 1. As you can see, there is no intersection of these two shaded regions. Answer: To obtain 8 ounces of a 32 % alcohol mixture we need to mix 4. Multiplying & Dividing Scientific Notation. O n eM5aPdaeO rw4ijtYhu MIKnCf8iYn0iQtWeW 1ANlfg9embQrFam 61r. 2) Flying with the wind a plane went 183 km/h. The perimeter of a rectangular field is 76ft. Learn. Graphing lines using slope-intercept form. We solve for x by adding 7 on both sides of the equation: x + 16 = 3x. Graph the inequality on a number line by drawing a circle over the number. Solving Inequalities. x y Entire Unit of Systems Worksheets, Activities, & Games -- includes 6 worksheets, a jeopardy review game, 2 "Maze" (A. Given a word problem, students will identify variables, write a system of linear inequalities, and graph the system, showing all possible combinations for the situation. We can graph the solutions of systems that contain nonlinear inequalities in a similar manner. Identify the slope constant in the inequality (the 'm' value). 250 solution of a linear Worksheet by Kuta Software LLC-2-3) Jane is selling apples and oranges. 4 x = 3. 4 + y− 4. Jan 27, 2024 · Inequality word problems worksheet answer key 50 inequality word problems worksheet Systems of inequalities word problems worksheet pdf. The solution to a system of linear inequalities is the same as the ordered pair used in linear inequalities. Step 3: Write an inequality to represent the income form the jewelry sold. Understand the Basic Concepts of Algebra I, II, Geometry, Statistics, and Trigonometry. Linear inequalities and systems of inequalities word problems. 31 nickels and 29 dimes. when inequalitites are graphed and multiple inequalities are graphed, to find answers that satisfy all of the inequaitites you will need to shade in a particular part of the graph. Spanish. Each joke worksheet includes a step-by-step answer key. Check Details. These types of problems can be simple or complex, but Let x = the number of bracelets sold. On the first day of ticket sales the school sold 9 adult tickets and 6 student tickets for a total of $165. -3-. 28 nickels and 32 dimes ____ 12. Step 4: Sarah knows that she will sell more than 50 bracelets. Equations algebraSystems of equations worksheets Problems inequalities inequality equations solving algebra variable guided solution tessshebayloVariable equations understanding. If we replace the equal sign by one of the inequality symbols,#, ,, $,or. Solving inequalities means finding all possible values of the variables. A common test point is the origin (0, 0). 2. How Systems of Equations Word Problems. Let y = the number of earrings sold. 50. View Answers. To check this solution, substitute. Write a system of inequalities that This is our system of equations. And so the answer would be no because her plan of getting D biscuits was not achieved. Permutations vs combinations. solve problems involving linear inequalities in two variables; and. This two page worksheet features 5 word problems that ask students to first write and then graph a system of inequalities. 5 and 8 Finding slope from a graph. tl fj sk ai df oi or rb kt uv