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6-4 Solving Special Systems (pp. 406–411)
EXERCISES
EXAMPLES
Classify each system. Give the number of solutions.
■
 y = 3x + 4

 6x - 2y = -8
Use the substitution method because the first
equation is solved for y.
6x - 2(3x + 4) = -8
Substitute 3x + 4 for y in
6x - 6x - 8 = -8
the second equation.
-8 = -8 ✓ True.
Solve each system of linear equations.

1x-3
y=_
4
28. 
_
y= 1x+5
4

 y = 3x + 2
30. 
 y = 2x
32.
The equation is an identity. There are infinitely
many solutions.
This system is consistent and dependent.
The two lines are coincident (the same line)
because they have identical slopes and
y-intercepts.
■
 y = 2x - 1

 2x - y = -2
 y = -x + 4

 x+y=4
31.
 -4x - y = 6
 _
 1 y = -2x - 3
2
33.
 y - 2x = -1

 y + 2x = -5
34. Tristan and his friend Marco just started DVD
collections. They continue to get DVDs at the rate
shown in the table below. Will Tristan ever have
the same number of DVDs as Marco? Explain.
 y = 2x - 1

 2x - y = -2
DVD Collections
Compare slopes and y-intercepts. Write both
equations in slope-intercept form.
⇒ y = 2x - 1
⇒ y = 2x + 2
The lines have the same slope and different
y-intercepts. The lines are parallel.
The lines never intersect, so this system is
inconsistent. It has no solution.
■
 x + 2y = 8

1x+4
 y = - _
2
29.
 2x - y = 6

 y=x-1
Month 1
Month 2
Month 3
Tristan
2
7
12
Marco
8
12
16
Classify each system. Give the number of solutions.

1x+2
y=_
2
35. 
_
y= 1x-8
4

37.
 2x + y = 2

 y - 2 = -2x
36.
 y = 3x - 7

 y = 3x + 2
38.
 -3x - y = -5

 y = -3x - 5
1y=3
 x + _
2
40. 
 2x = 6 - y
Write both equations in slope-intercept form.
 2x + 3y = 1
39. 
 3x + 2y = 1
 2x - y = 6
y=x-1

41. The two parallel lines graphed below represent a
system of equations. Classify the system and give
the number of solutions.
⇒ y = 2x - 6
⇒ y = 1x - 1
The lines intersect because they have different
slopes.
The system is consistent and independent.
There is one solution: (5, 4).
432
Untitled-9 432
Chapter 6 Systems of Equations and Inequalities
11/7/05 3:57:50 PM
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