Answer
All equations are true, so the solution is correct.
Work Step by Step
In order to verify that the order pair is a solution, we substitute the values of all 3 variables into all equations to ensure that they produce a true result:
$$ 3(2) + 3(-2) + 2(2)=4 \\ 4=4$$
For equation two:
$$2-3(-2)+2 =10 \\ 10=10$$
For equation three:
$$5(2)-2(-2)-3(2)=8 \\8=8$$
All equations are true, so the solution is correct.