Chapter 7 Review Sheet

Name__________________________________Algebra 1, Chapter 7 Review11/15/111. Use the system below to answer each question.(1 continued)d. Based on your graph in part c. estimate thesolution to the system. State how youdetermine your solution from the graph.x − 3y= −62x+ y = 9a. Is the point (–3, 1) a solution to thesystem? Show how you know.e. Solve the system algebraically by using themethod of substitution (not elimination).b. Express each equation in slope-interceptform.2. The graph of one equation in a system ofequations is shown below.6c. Graph the system using your equationsfrom part b or by finding two ordered pairsthat make each equation true. Label thecoordinates of two points on each line.8642-8 -6 -4 -2 2 4 6 8-2-4-6-842-6 -4 -2 2 4 6-2-4-6Write the equation of a line to form a systemwith the equation whose graph is shown sothat the system has the specified number ofsolutions. If not possible, explain why.a. No solutionb. Exactly 4 solutionsc. Exactly 2 solutions

3. Given the system:⎧6x− 2y= 10⎨⎩ y + 5 = 3x5. Use the system that is graphed below toanswer the following questions.a. Solve the system using the algebraicmethod of your choice.a. How many solutions does the systemhave?b. Based on your solution above, describewhat the graph of the system would looklike.State the solution set for the system ofequations.b. One of the equations in the system shown2is: y − 3 = − ( x + 2)Write the other equation in the system.4. Given the system:⎧3x+ y = 13⎨⎩2x− 4y= 18a. Solve the system using the method ofelimination. Show work.c. Use the results from part (b) toalgebraically verify your solution set(from part a) algebraically. Remember tocheck each solution in both equations!6. Consider this system of linear equations:2x− 5y= 74x− 3y= − 7b. Based on your solution above, describewhat the graph of the system would looklike.Explain why the method of substitution wouldbe a bad choice for solving the system

7. Consider the inequality y ≥ −x− 2 .a. Is the point (5, 7) a solution to theinequality? Show how you decide.b. Is the point ( − 8,1)a solution? Showhow you decide.8. Given the system of inequalities below:2x− 5y< 10x − y ≥ −1a. Is ( 0,0 ) a solution to the system? Justifyalgebraically.c. List two more solutions to the inequality.Show how you know they are solutions.b. Is ( − 2,1)a solution to the system?Justify algebraically.d. Using your result from part (c) above tohelp you, sketch the solution set below.Remember BLTs!c. List one more element of the solution set.Show how you know that your answer iscorrect.8642-8 -6 -4 -2 2 4 6 8-2-4-6-8e. How would the solution set you showedin part e change if the inequality werey > 3x+ 1?d. Solve the system by graphing. Clearlyindicate the solution set. BLTs!8642-8 -6 -4 -2 2 4 6 8-2-4-6-8

9. A system of linear inequalities is shownbelow.x ≤ 6, x ≥ 2, y ≥ −1( x )y − 5 ≤ − 1 − 22a. Is ( 0,0) a solution to the system?Justify.(10 continued)b. Solve the system of equations you wrotein part a. Be sure to check.c. What will be the cost if 2 girls haveSuperburgers and 6 girls have the subsandwich?b. Sketch a graph of the system and shadethe solution set.8c. The points in the solution set form theinterior and sides of what type ofpolygon?642-8 -6 -4 -2 2 4 6 8-2-4-6-811. Plot and label the points A(4, 6), B(-4, 4), andC(0, -4) on the graph provided below. Then,connect the points to create a triangle andshade the inside of the figure.8642-8 -6 -4 -2 2 4 6 8-2-4-6-8a. Write the equation of each boundary line.You may use slope-intercept form or pointslopeform.Line AB : Line BC :10. The coach took her basketball team out todinner at the end of the season. If five girlshave Superburgers and three girls havesubmarine sandwiches, the bill will be $10.00.If three girls have Superburgers and five girlshave submarines, the cost will be $10.80.a. Define variables to represent the cost ofthe Superburgers and the cost of the subsandwich. Write a system of equationsbased on the given information.Line AC :b. Convert the equations of the boundarylines above into a system of linearinequalities whose solution set is theshaded region. Use a point in the interiorof the triangle to determine how to writethe inequality.