Practice Test %2D Chapter 6

Graph each system and determine the number of solutions that it has. If it has one solution, name it.��y = 2x

y = 6 í x

62/87,21��To graph the system, write both equations in slope-intercept form. y = 2x y = íx + 6

The graph appears to intersect at the point (2, 4). You can check this by substituting 2 for x and 4 for y .

�

The solution is (2, 4).

��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10

62/87,21��To graph the system, write both equations in slope-intercept form. Equation 1:

Equation 2:

*UDSK�DQG�VROYH�� y = x í 4 y = íx + 10


�


��2x + 3y = 4 2x + 3y = í1

62/87,21��To graph the system, write both equations in slope-intercept form.Equation 1:

Equation 2:

Graph and solve.

The lines are parallel. So, there is no solution.

Use substitution to solve each system of equations.��y = x + 8

2x + y = í10

62/87,21��y = x + 8 2x + y = í10 Substitute x + 8 for y in the second equation. �

� Use the solution for x and either equation to find the value for y .�

� The solution is (í6, 2).

��x = í4y í 3 3x í 2y = 5

62/87,21��x = í4y í 3 3x í 2y = 5 Substitute í4y í 3 for x in the second equation. �

� Use the solution for y and either equation to find the value for x.�

� The solution is (1, í1).

��*$5'(1,1*� Corey has 42 feet of fencing around his garden. The garden is rectangular in shape, and its length isequal to twice the width minus 3 feet. Define the variables, and write a system of equations to find the length and width of the garden. Solve the system by using substitution.

62/87,21��Sample answer: Let w be the width and let �EH�WKH�OHQJWK��7KHQ��w + 2 = 42 and � ��w í 3. Substitute 2w í 3 for �LQ�WKH�ILUVW�HTXDWLRQ� �

� Use the solution for w and either equation to find the value for . �

� The width of the garden is 8 feet and the length is 13 feet.

��08/7,3/(�&+2,&(� Use elimination to solve the system. 6x í 4y = 6 í6x + 3y = 0

$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)

62/87,21��Because 6x and í6x have opposite coefficients, add the equations.�

� 1RZ��VXEVWLWXWH��í6 for y in either equation to find the value of x. �

� The solution is (í3, í6). So, the correct choice is B.

��6+233,1*� Shelly has $175 to shop for jeans and sweaters. Each pair of jeans costs $25, each sweater costs $20, and she buys 8 items. Determine the number of pairs of jeans and sweaters Shelly bought.

62/87,21��Let j = the number of pairs of jeans and s = the number of sweaters. Then, j + s = 8 and 25j + 20s = 175.Solve the first equation for j . �

Substitute 8 ± s for j in the second equation. �

� Now, substitute 5 for s in either equation to find the value of j . �

� Shelly bought 3 pairs of jeans and 5 sweaters.

Use elimination to solve each system of equations.��x + y = 13

x í y = 5

62/87,21��Because y and íy have opposite coefficients, add the equations.�

� Now, substitute 9 for x in either equation to find the value of y . �

� The solution is (9, 4).

��3x + 7y = 2 3x í 4y = 13

62/87,21��Because 3x and 3x have the same coefficients, multiply equation 2 by í1, then add the equations.

� Add the equations. �

Now, substitute í1 for y in either equation to find the value of x. �

The solution is (3, í1).

��x + y = 8 x í 3y = í4

62/87,21��Because x and x have the same coefficients, multiply equation 2 by ±1 and then add the equations.


� Now, substitute 3 for y in either equation to find the value of x. �


��2x + 6y = 18 3x + 2y = 13

62/87,21��Multiply the second equation by í3.

Now, because 6y and í6y have opposite coefficients, add the equations.�



��0$*$=,1(6� Julie subscribes to a sports magazine and a fashion magazine. She received 24 issues this year. Thenumber of fashion issues is 6 less than twice the number of sports issues. Define the variables, and write a system ofequations to find the number of issues of each magazine.

62/87,21��Let f = the number of fashion issues and s = the number of sports issues. So, f + s = 24 and f = 2s ± 6.Substitute 2s ± 6 for f in the first equation. �

� Now, substitute 10 for s in either equation to find the value of f . �

� So, Julie received 14 fashion issues and 10 sports issues.

Determine the best method to solve each system of equations. Then solve the system.��y = 3x

x + 2y = 21

62/87,21��y = 3x x + 2y = 21 � Substitute 3x for y in the second equation. �



��x + y = 12 y = x í 4

62/87,21��y = x ± 4 x + y = 12 � Substitute x ± 4 for y in the second equation. �



��x + y = 15 x í y = 9

62/87,21��Because the y-terms have opposite coefficients, add the equations.�

� 1RZ��VXEVWLWXWH�� for x in either equation to find the value of y . �


��3x + 5y = 7 2x í 3y = 11

62/87,21��Because none of the terms are opposites, use elimination by multiplication to solve. Multiply the first equation by 2and the second equation by -3. Then add the equations to eliminate the x-term. 3x + 5y = 7 2x í 3y = 11 �

�

� �

� Substitute -1 for y in the second equation to find x. �

� The solution is (4, ±1).

��OFFICE SUPPLIES At a sale, Ricardo bought 24 reams of paper and 4 inkjet cartridges for $320. Britney bought 2 reams of paper and 1 inkjet cartridge for $50. The reams of paper were all the same price and the inkjet cartridges were all the same price. Write a system of equations to represent this situation. Determine the best method to solve the system of equations. Then solve the system.

62/87,21��24p + 4c = 320 2p + c = 50 � Solve equation 2 for c. c = 50 ± 2p � Substitute 50 ± 2p for c in the other equation.�

� Substitute 7.5 for p in equation 2. c = 50 ± 2(7.5) c = 50 ± 15 c = 35 � paper: $7.50; cartridge: $35

Solve each system of inequalities by graphing.��x > 2

y < 4

62/87,21��*UDSK�HDFK�LQHTXDOLW\�� The graph of x > 2 is dashed and is not included in the graph of the solution.

�7KH�JUDSK�RI�y ��LV�DOVR�GDVKHG�DQG�LV�QRW�LQFOXGHG�LQ�WKH�JUDSK�RI�WKH�VROXWLRQ��

The solution of the system is the set of ordered pairs in the intersection of the graphs of x > 2 and y < 4. Overlay the graphs and locate the green region. This is the intersection.

� The solution region is shaded in gray.

��x + y �� y ��x + 2

62/87,21��*UDSK�HDFK�LQHTXDOLW\�� The graph of x + y ��LV�VROLG�DQG�LV�LQFOXGHG�LQ�WKH�JUDSK�RI�WKH�VROXWLRQ��

The graph of y ��x + 2 is also solid and is included in the graph of the solution.

The solution of the system is the set of ordered pairs in the intersection of the graphs of x + y ��DQG�y ��x + 2. Overlay the graphs and locate the green region. This is the intersection.

The solution region is shaded in gray.

��3x í y > 9 y > í2x

62/87,21��*UDSK�HDFK�LQHTXDOLW\�� The graph of 3x í y �!��LV�GDVKHG�DQG�LV�QRW�LQFOXGHG�LQ�WKH�JUDSK�RI�WKH�VROXWLRQ��

The graph of y > í2x�LV�DOVR�GDVKHG�DQG�LV�QRW�LQFOXGHG�LQ�WKH�JUDSK�RI�WKH�VROXWLRQ��

The solution of the system is the set of ordered pairs in the intersection of the graphs of 3x í y > 9 and y > í2x. Overlay the graphs and locate the green region. This is the intersection.


��y ��x + 3 í4x í 3y > 12

62/87,21��Graph each inequality. �7KH�JUDSK�RI�y ��x��LV�VROLG�DQG�LV�LQFOXGHG�LQ�WKH�JUDSK�RI�WKH�VROXWLRQ��

The graph of í4x í 3y �!��LV�GDVKHG�DQG�LV�QRW�LQFOXGHG�LQ�WKH�JUDSK�RI�WKH�VROXWLRQ��

The solution of the system is the set of ordered pairs in the intersection of the graphs of y ��x + 3 and í4x í 3y > 12. Overlay the graphs and locate the green region. This is the intersection.


eSolutions Manual - Powered by Cognero Page 1

Practice Test - Chapter 6


y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12








y = 6 í x



�


��y = x í 3 y = í2x + 9

62/87,21��y = x í 3 y = í2x + 9


�


��x í y = 4 x + y = 10


Equation 2:



�


��2x + 3y = 4 2x + 3y = í1


Equation 2:

Graph and solve.



2x + y = í10




��x = í4y í 3 3x í 2y = 5









$��(5, 6) %��(í3, í6) &��(1, 0) '��(4, í8)










x í y = 5




��3x + 7y = 2 3x í 4y = 13





��x + y = 8 x í 3y = í4





��2x + 6y = 18 3x + 2y = 13










x + 2y = 21




��x + y = 12 y = x í 4




��x + y = 15 x í y = 9




��3x + 5y = 7 2x í 3y = 11


�

� �







y < 4





��x + y �� y ��x + 2





��3x í y > 9 y > í2x





��y ��x + 3 í4x í 3y > 12







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Practice Test %2D Chapter 6