Answer
No Solution.
Work Step by Step
$4x-y+3z=10$ Equation $(1)$
$x+y-z=5$ Equation $(2)$
$8x-2y+6z=10$ Equation $(3)$
Equation $(1)$ $+$ Equation $(2)$
$(4x-y+3z) + (x+y-z) = (10+5)$
$5x+2z=15$ Equation $(4)$
$2\times$ Equation $(2)$ $+$ Equation $(3)$
$2(x+y-z)=2\times5$
$(2x+2y-2z) + (8x-2y+6z) = (10+10)$
$10x+4z=20$ Equation $(5)$
$2\times$ Equation $(4)$ $-$ Equation $(5)$
$2(5x+2z) = 2\times15$
$(10x+4z) - (10x+4z) = (30-20)$
$0 = 10$
Since the above statement is not true, the equations are parallel and have no solution.
