Answer
No Solution.
Work Step by Step
$4x-y+2z=5$ Equation $(1)$
$2y+z=4 $ Equation $(2)$
$4x+y+3z=10$ Equation $(3)$
Multiply Equation $(1)$ by $2$ then add with Equation $(2)$ to eliminate $y$
$2(4x-y+2z)+2y+z=2(5)+4 $
$8x-2y+4z+2y+z=10+4 $
Combine like terms.
$8x+5z=14$ Equation $(4)$
Multiply Equation $(3)$ by $-2$ then add with Equation $(2)$ to eliminate $y$
$-2(4x+y+3z)+2y+z=-2(10)+4 $
$-8x-2y-6z+2y+z=-20+4 $
Combine like terms.
$-8x-5z=-16$ Equation $(5)$
Add Equation $(4)$ and Equation $(5)$
$8x+5z-8x-5z=14-16$
$0=-2$
Since the statement is not true, this system is inconsistent and has no solution.