Answer
$(-3,-2,5)$
Work Step by Step
$2x-3y+z=5$ Equation $(1)$
$x+y+z=0$ Equation $(2)$
$4x+2y+4z=4$ Equation $(3)$
Multiply Equation $(2)$ by $3$ and add with Equation $(1)$
$3(x+y+z)+2x-3y+z=3(0)+5$
$3x+3y+3z+2x-3y+z=5$
Combine like terms.
$5x+4z=5$ Equation $(4)$
Multiply Equation $(2)$ by $-2$ and add with Equation $(3)$
$-2(x+y+z)+4x+2y+4z=-2(0)+4$
$-2x-2y-2z+4x+2y+4z=4$
Combine like terms.
$2x+2z=4$ Equation $(5)$
Multiply Equation $(4)$ by $2$, Equation $(5)$ by $-4$ and add the resultant equations.
$2(5x+4z)-4(2x+2z)=2(5)-4(4)$
$10x+8z-8x-8z=10-16$
Combine like terms.
$2x=-6$
$x=-3$
Substitute $x$ value in Equation $(5)$
$2x+2z=4$
$2(-3)+2z=4$
$-6+2z=4$
$2z=10$
$z=5$
Substitute $x$ and $z$ values in Equation $(2)$
$x+y+z=0$
$-3+y+5=0$
$y+2=0$
$y=-2$
$(-3,-2,5)$ satisfies the given equations.
Solution: $(-3,-2,5)$
