Answer
$x=-\frac{1}{2}$
$y=1$
$z=2$
Work Step by Step
Use elimination for the equations:
$-2x + 5y - 2z = 2$
$2x - 4y + 3z= 1$
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$y+z=3$ (1)
$2x - 4y + 3z= 1$
$6x + 2y + 10z = 19$
Multiply the first equation by $-3$:
$-6x +12y -9z= -3$
$6x + 2y + 10z = 19$
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$14y+z=16$ (2)
From (1) and (2):
$y+z=3$
$14y+z=16$
Multiply both sides of the first equation by $-1$
$-y-z=-3$
$14y+z=16$
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$13y=13$
$y=1$
Solve for z: $1+z=3$
$z=2$
Solve for x: $2x-4(1)+3(2)=1$
$2x=-1$
$x=-\frac{1}{2}$
