Answer
Answer A
Work Step by Step
The second equation: $3x - y + 4z = 8 $
$\rightarrow y=3x+4z-8$
Substitute for x in the first equation:
$2x + 5y + 3z = 10$
$2x + 5(3x+4z-8) + 3z = 10$
$2x+15x+20z-40+3z=10$
$17x+23z=50$ (1)
Substitute for x in the third equation:
$5x - 2y + 7z = 12$
$5x-2(3x+4z-8)+7z=12$
$5x-6x-8z+16+7z=12$
$-x-z=-4$
$\rightarrow x=-z+4$
Substitute for x in equation (1):
$17(-z+4)+23z=50$
$-17z+68+23z=50$
$6z=-18$
$z=-3$
Solve for x: $x=-(-3)+4=7$
Solve for y: $y=3.7+4(-3)-8=1$
$(7,1,-3)$ is the solution of the system.
The correct answer is A.
