SOLUTION: I'm stuck on a problem in my algebra test. - Solve each system of equations. - 5x = -15 -11x - 4y + 7z = 1 3x - 3y + z = 1 - A) x=3, y=-19, z=41 B) x=42, y=-33, z=-13

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Question 773139: I'm stuck on a problem in my algebra test.
-
Solve each system of equations.
-
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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