How do I solve this 3 variable by substitution problem?

Question

Solve for x, y, and z

5x+2y-3z=-12

x-4y+2z=23

3x+y-7z=-22

Please show step by step

Answer 1

1) 5x + 2y - 3z = -12

2) x - 4y + 2z  = 23

3) 3x + y - 7z = -22

multiply eq(1) by 2, add to eq(2):

10x + 4y - 6z = -24

  x - 4y + 2z  = 23

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11x     - 4z     = -1   (a)

multiply eq(3) by 4, add to eq(2):

12x + 4y - 28z = -88

   x  -  4y  +  2z =  23

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13x    - 26z    =  -65   (b)

solve for x in eq(a):

11x = 4z - 1

x = (4z - 1)/11

substitute into eq(b):

13((4z - 1)/11) - 26z  = -65

(52z - 13)/11 - 286z/11 = -715/11

52z - 13 - 286z  = -715

-234z = -702

z = -702/-234 = 3

using eq(a):

11x - 4(3) = -1

11x - 12 = -1

11x = 11

x = 1

using eq(2):

1 - 4y + 2(3) = 23

-4y = 16

y = -4

check using eq(1):

5(1) + 2(-4) - 3(3) = -12

5 - 8 - 9 = -12

-12 = -12

x = 1, y = -4, z = 3  or (1,-4,3)