Answer
Answer B
Work Step by Step
Using elimination for the first two equations:
$2x - 2y - z = 6$
$-x + y + 3z =-3$
Multiply both sides of the first equation by $3$
$6x - 6y - 3z = 18$
$-x + y + 3z =-3$
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$5x-5y=15$ (1)
Using elimination for the first and the third equations:
$2x - 2y - z = 6$
$3x - 3y + 2z = 9$
Multiply both sides of the first equation by $2$:
$4x - 4y - 2z = 12$
$3x - 3y + 2z = 9$
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$7x-7y=21$ (2)
From (1) and (2) we get the system of equations:
$5x-5y=15$
$7x-7y=21$
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$x-y=3$
$x-y=3$
Hence $y=x-3$
Solve for z: $-x + y + 3z =-3$
$-x+x-3+3z=-3$
$3z=0$
$z=0$
$(x,x-3,0)$ is the solution of the system.
The correct answer is B.
