Pre Cal.--Check my work?

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Solve the system of equations: x - y - z = 2; x + 2y - 2z = 3; 3x - 2y - 4z = 5?

well, you have:
1- x-y-z=2
2- x+2y-2z=3
3- 3x-2y-4z=5

multiply both sides of the equation 1 by 2:
x-y-z=2 ===> 2x-2y-2z=4

add this by equation 2:

2x-2y-2z=4
x+2y-2z=3

==> 3x - 4z = 7 (*)

now, multiple both sides of equation 1 by -2:
x-y-z=2
==> -2x + 2y + 2z = -4
add this by equation 3:
-2x + 2y + 2z = -4
3x-2y-4z=5
===> x - 2z = 1

great. now you have
x - 2z = 1
and
3x - 4z = 7

so , multiple both sides of the first one by -2:
-2x + 4z = -2
3x - 4z = 7
===> (add them together) x = 5

3x - 4z = 7 ===(x=5)=> 15 - 4z = 7 ==> 4z = 8 ==> z=2



x-y-z= 2 ===> 5-y-2 = 2 ==> y=1

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