Chapter 8 Systems Of Linear Equations And Inequalities Worksheet With Answers Page 8
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2
3
4
5
6
7
8
9
10(8–9)
401
8.1 Solving Systems by Graphing and Substitution
8 . 1
E X E R C I S E S
Reading and Writing After reading this section, write out
a)
b)
the answers to these questions. Use complete sentences.
y
y
1. How do we solve a system of linear equations by
3
3
graphing?
2
2
1
1
2. How can you determine whether a system has no solu-
x
x
– 4
– 3
– 2
– 1
– 4
– 3
– 2
1 2
tion by graphing?
– 1
– 2
– 2
3. What is the major disadvantage to solving a system by
– 3
– 3
graphing?
c)
d)
4. How do we solve systems by substitution?
y
y
4
5. How can you identify an inconsistent system when solv-
1
3
ing by substitution?
2
– 2
– 1
x
1
3 4
– 1
– 2
x
– 1
1 2 3 4
– 1
6. How can you identify a dependent system when solving
– 4
– 2
by substitution?
Solve each system by the substitution method. Determine
whether the equations are independent, dependent, or incon-
sistent. See Examples 4–6.
Solve each system by graphing. See Examples 1–3.
21. y
x
5
22. y
x
4
7. y
2x
8. y
x
3
2x
5y
1
3y
5x
6
y
x
3
y
x
1
23. x
2y
7
24. x
y
3
9.
y
2x
1
10. y
2x
1
3x
2y
5
3x
2y
4
2y
x
2
x
y
2
25. x
y
5
26. 2x
y
3
11. y
x
3
12. y
3x
2x
2y
14
2y
4x
6
x
2y
4
x
y
2
13. 2y
2x
2
14. 3y
3x
9
27. y
2x
5
28. 3x
6y
5
2y
2x
6
x
y
1
y
1
2(x
2)
2y
4x
6
1
15. y
x
4
16. 2x
3y
6
29. 2x
y
9
30. 3y
x
0
2
2x
5y
15
x
4y
2
2
x
2y
8
y
x
2
3
31.
x
y
0
32. 2y
x
6
2x
3y
35
3x
2y
2
The graphs of the following systems are given in (a) through
(d). Match each system with the correct graph.
33.
x
y
40
34.
x
y
10
0.1x
0.08y
3.5
0.2x
0.05y
7
17. 5x
4y
7
18. 3x
5y
9
x
3y
9
5x
6y
8
35. y
2x
30
36. 3x
5y
4
1
1
3
19. 4x
5y
2
20. 4x
5y
2
x
y
1
y
x
2
3y
x
3
4y
x
11
5
2
4
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