The starting system of equations is
6x - 5y = -30 (1)
2x + 2y = 12 (2)
Multiply equation (2) by 3 (both sides). Keep equation (1) as is. You get
6x - 5y = -30 (3)
6x + 6y = 36 (4)
Now equations (3) and (4) have the same coefficient at x.
Therefore, you subtract equation (3) from equation (4), and you annihilate the terms "6x" this way.
You get then
6y - (-5y) = 36 - (-30)
11y = 66
y = 66/11 = 6.
Then from equation (2)
2x = 12 - 2y = 12 - 2*6 = 0.
ANSWER. x = 0, y = 6.
Solved.
You may check it that the answer is correct
by substituting the found values in original equations.
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It looks like you need to learn (to get familiar with) the general theory/technique on solving systems of two equations in two unknown.
