Answer:
x = 13
y = -10
z = -7
Step-by-step explanation:
x+y+z=−4
2x+3y−2z=10
−x+2y−3z=−12
Add the first and the third equations to eliminate x
x+y+z=−4
−x+2y−3z=−12
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3y -2z = -16 Equation A
Add the second and twice the third equation to eliminate x
2x+3y−2z=10
−2x+4y−6z=−24
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7y -8z = -14 Equation B
Take Equation A and multiply by -4
-4*( 3y -2z) = (-16)*-4
-12y + 8z = 64
Add this to Equation B
-12y + 8z = 64
7y -8z = -14
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-5y = 50
Divide by -5
-5y/-5 = 50/-5
y = -10
Now using equation A
3y -2z = -16
3*-10 -2z = -16
-30 -2z = -16
Add 30 to each side
-2z = -16+30
-2z = 14
Divide by -2
-2z/-2 = 14/-2
z = -7
Now find x using the first equation
x+y+z = -4
x -7-10 = -4
x -17 = -4
Add 17 to each side
x-17+17 = -4+17
x = 13
