Question

x-y+3z=13 
4x+y+2z=17 
3x+2y+2z=1 

Answer 1

I am labeling the equations 1,2,3

1.   x -    y + 3z = 13

2. 4x +   y + 2z = 17

3. 3x + 2y + 2z =   1

(2-3)

 4x +  y + 2z = 17

-3x - 2y -2z  = -1

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x - y = 16

x = 16 - y

++++++++++++++++++++++++

substitute x into 1.

x - y + 3z = 13

-----------------------

16 - y -y + 3z = 13

-2y + 3z = -3  label (1a)

++++++++++++++++++++++++++++++

substitute x into 2.

4x + y +2z = 17

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4(16 - y) + y + 2z = 17

64 - 4y + y + 2z = 17

-3y + 2z = -47 label this (2a.)

+++++++++++++++++++++++++++++++++

substitute x into 3

3x + 2y +2z = 1

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3(16 - y) + 2y + 2z = 1

48 -3y + 2y + 2z = 1

-y + 2z = -47  label (3a.)

++++++++++++++++++++++++++++++++

(2a - 3a)  lets us solve for y

  -3y + 2z = -47

+   y  - 2z = 47

-2y = 0

y = 0  

++++++++++++++++++++++++++++++++++++

substitute y = 0 into 1a.  (because we used 2a and 3a to solve for y

-2y + 3z = -3

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-2(0) + 3z = -3

z = -1

++++++++++++++++++++++++++++++++++++++

substitute y = 0 and z = -1 into 1.

x - y +3z = 13

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x - 0 + 3 (-1) = 13

x - 3 = 13

x = 10

+++++++++++++++++++++++++++++++++==

x = 10, y = 0 , z = -1