First, let's clear z from equation 1:
Now, let's plug it in equations 2 and 3, respectively:
We'll have a new system of equations:
Now, let's simplify each equation. To do so, we'll multiply the first one by -2/5 and the second one by -2/17. We'll get:
Now, let's solve each equation for y to see them as a pair of line equations:
Notice that this lines have the same slope. Therefore, they're parallel and do not intercept.
This way, we can conlcude that the original system has no solution.