# How do you solve the system of equations x+y+z=1, x+2y+z=2, x-y+z=-5 ?

Mar 18, 2017

This system has no solutions.

#### Explanation:

Given:

$\left\{\begin{matrix}x + y + z = 1 \\ x + 2 y + z = 2 \\ x - y + z = - 5\end{matrix}\right.$

Adding the first and third equations, we get:

$2 x + 2 z = - 4$

Hence:

$x + z = - 2 \text{ } \ldots$ (i)

Adding twice the third equation to the second equation, we get:

$3 x + 3 z = - 8$

Hence:

$x + z = - \frac{8}{3} \text{ } \ldots$ (ii)

Equations (i) and (ii) are incompatible, since $- 2 \ne - \frac{8}{3}$

So there is no solution to this system of equations.