0-5 Systems of Linear Equations and Inequalities

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1. Solve each system of equations by graphing. Graph each equation in the system. The lines intersect at the point (1, 3). This ordered pair is the solution of the system. CHECK esolutions Manual - Powered by Cognero Page 1

3. Solve each equation for y. Then graph each equation. The lines intersect at the point (2, 4). This ordered pair is the solution of the system. CHECK esolutions Manual - Powered by Cognero Page 2

5. Solve each equation for y. Then graph each equation. The lines intersect at the point ( 3, 2). This ordered pair is the solution of the system. CHECK esolutions Manual - Powered by Cognero Page 3

7. Use substitution to solve each system of equations. To solve the system by substitution, first solve one equation for x or y. In this case, y is easiest to solve for in the first equation. Then substitute this expression for y into the other equation and solve for x. Substitute this value for x into the equation you solved for y to find the value of y. The solution is (3, 1). 9. To solve the system by substitution, substitute the expression given for y into the other equation and solve for x. Substitute this value for x into the first equation to find the value of y. The solution is (5.25, 0.75). esolutions Manual - Powered by Cognero Page 4

11. To solve the system by substitution, first solve one equation for x or y. In this case, x is easiest to solve for in the second equation. Then substitute this expression for x into the other equation and solve for y. Substitute this value for y into the equation you solved for x to find the value of x. The solution is (9, 6). esolutions Manual - Powered by Cognero Page 5

13. JOBS Connor works at a movie rental store earning $8 per hour. He also walks dogs for $10 per hour on the weekends. Connor worked 13 hours this week and made $110. How many hours each did he work at the movie rental store? How many hours did he walk dogs over the weekend? Use the information given to write a system of equations. Let x be the number of hours Connor works at the movie store per week and y be the number of hours he walks dogs per week. If he worked 13 hours this week then x + y = 13. If he earns $8 per hour at renting movies, $10 per hour walking dogs, and he made a total of $110 this week working these two jobs, then 8x + 10y = 110. Therefore, a system of equations representing this situation is. To solve this system, solve the first equation for y. Then substitute this expression for y into the other equation and solve for x. Substitute this value for x into the equation you solved for y to find the value of y. The solution is (10, 3), which means that Connor worked 10 hours at the movie rental store and 3 hours walking dogs. esolutions Manual - Powered by Cognero Page 6

14. Use elimination to solve each system of equations. Eliminate the variable y in the system by adding the two equations. Substitute this value for x into one of the original equations and solve for y. The solution is (2, 5). 15. Eliminate the variable x in the system by multiplying the first equation by 2 and then adding the two equations. Substitute this value for y into one of the original equations and solve for x. The solution is (8, 5). esolutions Manual - Powered by Cognero Page 7

16. Eliminate the variable x in the system by multiplying the first equation by 2, multiplying the second equation by 3, and then adding the two equations. Substitute this value for y into one of the original equations and solve for x. 17. The solution is (5, 2). Eliminate the variable y in the system by multiplying the first equation by 5 and then adding the two equations. Substitute this value for x into one of the original equations and solve for y. The solution is. esolutions Manual - Powered by Cognero Page 8

18. Eliminate the variable y in the system by multiplying the second equation by 2 and then adding the two equations. Substitute this value for x into one of the original equations and solve for y. The solution is. 19. Eliminate the variable y in the system by multiplying the second equation by 2 and then adding the two equations. Substitute this value for x into one of the original equations and solve for y. The solution is ( 4, 5). esolutions Manual - Powered by Cognero Page 9

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