Answer
This system is inconsistent - it has not solutions.
Work Step by Step
Follow the steps below
Step 1: Add to the third equation the first one multiplied by $4/3$ to eliminate $x$:
$$4x+\frac{4}{3}(-3x)-8y+\frac{4}{3}5y = 32 +\frac{4}{3}(-22)$$ which becomes
$$-8y+\frac{20}{3}y = 32-\frac{88}{3}\Rightarrow -\frac{4}{3}y = \frac{8}{3}$$
and this gives $$y=-2.$$
Step 2: Add the 1st equation to the second to eliminate $x$:
$$3x-3x+4y-5y=4-22$$
which gives $$y= 18.$$
Now note that this is in contradiction with what we got in the step one since $y$ cannot be both $-2$ and $18$ so this system is inconsistent and has no solutions.
