Answer
All equations are true, so the solution is correct.
Work Step by Step
In order to verify that the point is a solution, we substitute the values of all 3 variables into all equations to ensure that they produce a true result:
$$ 4(4) - 5(2) =6 \\6=6$$
For equation two:
$$5(-3) -2 =-17 \\ -17=-17$$
For equation three:
$$-4-6(-3)+5(2)= 24 \\ 24=24$$
All equations are true, so the solution is correct.