Question

X+y+3z=-4
-x+y-2z=5
2x-z=-3

Answer 1

x = -2, y = 1, z = -1

Explanation:

`- \begin{cases}x + y + 3z = -4 \\ -x + y - 2z = 5 \\ 2x - z = -3\end{cases} \text{ / Subtract all of the equations} \\ \\\to x + y + 3z - (-x + y - 2z) - (2x - z) = -4 - 5 - (-3) \\ \\\to x + y + 3z + x - y + 2z - 2x + z = -4 - 5 + 3 \\ \\\to 6z = -6 \\ \\\to z = -1 \\ \\\text{Substitute z = -1 into the 3rd equation to find x:} \\ \2x + 1 = -3 \\\to 2x = -4 \\\to x = -2 \\ \\\text{Substitute z = -1, x = -2 into the first equation to find y:} \\-2 + y - 3 = -4 \\\to y - 5 = -4 \\\to y = 1`