Solve each system by the substitution method. Check each solution. See Examples 1–5.
SECTION 4.2 Solving Systems of Linear Equations by Substitution 263
3. 4. 5.
x=y+ 43 x+ 2 y= 27
y=- 5 xx+ 3 y=- 28
y= 3 xx+y= 126. 7. 8.
x+ 3 y= 02 x- 5 =-y
2 x+y= 03 x+ 4 =-y
x=y- 34 x+ 3 y=- 59. 10. 11.
x- 2 y=- 103 x+ 5 y= 25
x+ y= 83 x- 2 y= 19
x+ y= 17 x+ 4 y= 1312. 13. 14.
y= 4 x+ 34 x-y=- 3
y= 3 x- 53 x-y= 5
2 x- y=- 65 x+ 2 y=- 1515. 16. 17.
x= 8 - 4 y2 x+ 8 y= 3
4 x+ 2 y= 3x+ y= 0
4 x- 2 y= 22 x+ y= 018. 19. 20.
3 x+y= 72 y= 14 - 6 x
2 x-y=- 122 y= 4 x+ 24
x= 1 - 5 y2 x+ 10 y= 3Solve each system by the substitution method. Check each solution. See Examples 6 and 7.
1
2x+ 2 y=- 71
2
x+1
3
y=-1
3
y= 5 x1
4
x-1
5
y= 9y= 3 x1
2
x+1
3
y= 324. 25. 26.
x
4-
3 y
2=
9
4
x
2+
y
3=
7
6
3 x
5+
y
2=-
7
10
x
5+ 2 y=8
5
-
1
2
x-1
3
y=- 51
6
x+1
6
y= 127. 28. 29.
- 0.1x+2.7y=9.8
0.2x-1.3y=-3.21
3x-1
12
y=-1
6
1
2
x-1
8
y =-1
4
1
4
x+1
2
y= 121
6
x+1
3
y= 830. 31. 32.
2.2x+1.5y=8.90.8x-0.1y=1.3
0.6x+0.3y=-0.30.3x-0.1y=2.1
0.5x-0.2y=4.10.1x+0.9y=- 2EXERCISES 33–36FOR INDIVIDUAL OR GROUP WORK
A system of linear equations can be used to model the cost and the revenue of a business.
Work Exercises 33–36 in order.
33.Suppose that you start a business manufacturing
and selling bicycles, and it costs you $5000 to
get started. Each bicycle will cost $400 to
manufacture. Explain why the linear equation
( in dollars)
gives your totalcost of manufacturing xbicycles.
34.You decide to sell each bike for $600. Write an equation using (in dollars) to
express your revenue when you sell xbikes.
35.Form a system from the two equations in Exercises 33 and 34.Solve the system.
36.The value of xfrom Exercise 35is the number of bikes it takes to break even.Fill
in the blanks: When bikes are sold, the break-even point is reached. At that
point, you have spent dollars and taken in dollars.y 2y 1 = 400 x+ 5000 y 1