9. 10. 11.
x+ y= 0
4 x+ 2 y= 0
1 0, 0 2
3 y=- 2 x- 4
5 y= 3 x+ 20
1 - 5, 2 2
3 y= 2 x+ 30
1 6, - 82
254 CHAPTER 4 Systems of Linear Equations and Inequalities
12.Concept Check When a student was asked to determine whether the ordered pair
is a solution of the following system, he answered “yes.” His reasoning was that
the ordered pair satisfies the equation since WHAT
WENT WRONG?
13.Concept Check Each ordered pair in (a) – (d) is a solution of one of the systems graphed
in A – D. Because of the location of the point of intersection, you should be able to deter-
mine the correct system for each solution. Match each system from A – D with its solution
from (a) – (d).
(a) A. B.
(b)
(c) C. D.
(d) 1 5, - 22
1 - 3, 2 2
1 - 2, 3 2
1 3, 4 2
2 x+y= 4
x+y=- 1
x+y=-1, 1 + 1 - 22 =-1.
1 1, - 22
073
–7
3
x
y
x – y = 7
x – y = 7
x + y = 3
x + y = 3
x
y
–1 0
1
7
7
x – y = –1
x – y = –1
x + y = 7
x + y = 7
x
y
x – y = –5
x – y = –5
x + y = 1
x + y = 1
–5 1
1
5
0 x
y
x + y = –1
x – y = –5
–5
5
x + y = –1
–1
–1
x – y = –5
14.Concept Check The following system has infinitely many solutions. Write its solution
set, using set-builder notation as described in Example 3(b).
Solve each system of equations by graphing. If the system is inconsistent or the equations are
dependent, say so. See Examples 2 and 3.
3 x- 2 y= 4
6 x- 4 y= 8
15. 16. 17.
y-x= 4
x+y= 4
x+y=- 1
x-y= 3
x+y= 6
x-y= 2
18. 19. 20.
4 x+y= 2
2 x-y= 4
x+ 2 y= 2
x- 2 y= 6
y-x=- 5
x+y=- 5
21. 22. 23.
y=- 3 x+ 2
2 x- 3 y=- 6
2 x+ 3 y= 12
2 x- y= 4
3 x- 2 y=- 3
24. 25. 26.
2 x+ 4 y= 12
x+ 2 y= 4
4 x- 2 y= 8
2 x- y= 6
y=x- 3
27. 28. 29.
y=-
3
2
x+ 3
3 x- 4 y= 24
4 x- 2 y= 8
2 x- y= 4
6 x+ 2 y= 10
3 x+ y= 5
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