6-2 Solving Systems by Substitution (pp. 390–396)
EXERCISES
EXAMPLE
■
 2x - 3y = -2
Solve 
 y - 3x = 10
by substitution.
Step 1 y - 3x = 10
y = 3x + 10
Solve the second
equation for y.
2x - 3y = -2
Step 2
2x - 3(3x + 10) = -2
Step 3 2x - 9x - 30 = -2
-7x - 30 = -2
-7x = 28
x = -4
Step 4
y - 3x = 10
y - 3(-4) = 10
y + 12 = 10
y = -2
Step 5 (-4, -2)
Substitute 3x + 10
for y in the first
equation.
Solve for x.
Substitute -4 for x.
Solve each system by substitution.
y=x+3
 y = -4x
13. 
14. 
 y = 2x + 12
 y = 2x - 3
15.
 2x + y = 4

 3x + y = 3
16.
 x + y = -1

 y = -2x + 3
17.
x=y-7

 -y - 2x = 8
18.
1x+y=9
 _
2
 3x - 4y = -6
19. The Nash family’s car needs repairs. Estimates
for parts and labor from two garages are shown
below.
Find the value of y.
Write the solution as an
ordered pair.
Garage
Parts ($)
Labor ($ per hour)
Motor Works
650
70
Jim’s Car Care
800
55
For how many hours of labor will the total cost of
fixing the car be the same at both garages? What
will that cost be? Which garage will be cheaper if
the repairs require 8 hours of labor? Explain.
To check the solution, substitute (-4, -2) into
both equations in the system.
6-3 Solving Systems by Elimination (pp. 397–403)
EXERCISES
EXAMPLE
■
 2x - 3y = -8
Solve 
Step 1
Step 2
Step 3
 x + 4y = 7
by elimination.
2x - 3y = -8
+(-2)(x + 4y = 7)
−−−−−−−−−−−−−−
2x - 3y = -8
+(-2x - 8y = -14)
−−−−−−−−−−−−−
0x - 11y = -22
y=2
2x - 3y = -8
2x - 3(2) = -8
2x - 6 = -8
2x = -2
x = -1
Step 4 (-1, 2)
Multiply the
second
equation by -2.
Eliminate the
x-term.
Solve for y.
Substitute 2 for y.
Simplify and solve
for x.
Write the solution as
an ordered pair.
Solve each system by elimination.
 4x + y = -1
 x + 2y = -1
20. 
21. 
 2x - y = -5
 x+y=2
22.
 x + y = 12

 2x + 5y = 27
23.
 3x - 2y = -6
_
 1 x + 3y = 9
3
Solve each system by any method. Explain why you
chose each method. Check your answer.
 3x + y = 2
24. 
 y = -4x
26.
 2y = -3x

 y = -2x + 2
1x-6
 y = _
3
25. 
 y = -2x + 1
27.
x-y=0

 3x + y = 8
To check the solution, substitute (-1, 2) into both
equations in the system.
Study Guide: Review
Untitled-9 431
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11/7/05 3:57:47 PM