Question 773139: I'm stuck on a problem in my algebra test.
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Solve each system of equations.
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5x = -15
-11x - 4y + 7z = 1
3x - 3y + z = 1
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A) x=3, y=-19, z=41
B) x=42, y=-33, z=-13
C) x=-45, y=-14, z=-40
D) x=-3, y=-7, z=1
E) x=-3, y=-6, z=-8
F) x=38, y=22, z=-26
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I know that x = -3, and I've tried substituting this into the other two equations, then solving one into the other, but it doesn't match any of the answers! Could I have some help? Thank you for your time!
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
(1) 5x = -15
(2) -11x - 4y + 7z = 1
(3) 3x - 3y + z = 1
Solve (1) for x
5x = -15
x = -3
Substitute x = -3 in (2)
-11x - 4y + 7z = 1
-11(-3) - 4y + 7z = 1
33 - 4y + 7z = 1
(4) -4y + 7z = -32
Substitute x = -3 in (3)
3x - 3y + z = 1
3(-3) - 3y + z = 1
-9 - 3y + z = 1
(5) -3y + z = 10
So you have this system:
(4) -4y + 7z = -32
(5) -3y + z = 10
Solve (5) for z
-3y + z = 10
(6) z = 10 + 3y
Substitute in (4)
-4y + 7z = -32
-4y + 7(10 + 3y) = -32
-4y + 70 + 21y = -32
17y + 70 = -32
17y = -102
y = -6
Substitute in (6)
(6) z = 10 + 3(-6)
z = 10 - 18
z = -8
Answer: E) x=-3, y=-6, z=-8
Edwin
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