How do you solve simultaneous equtions?

Say you had two equtions to solve simultaneously.

Example 1: x + 5y = -7; 2x - 2y = 10

Multiply one of the equtions so that one of the variables has the same coefficient. In this example, I would multiple the first eqution by 2 to get 2x + 10y = -14. That way, I can cancel this new equation with equation 2.

So new equation - equation 2 = 2x + 10 y - (2x - 2y) = -14 - 10

                                                = 12y = -24

                                                = y = -2

Then plug y=3 to the first equation to get what the value of x is. x + 5(-2) = -7 so x = -7 + 10 = 3

And then double check that the second equation is true for these values. I.e: when x = 3 and y = -2,

2(3) - 2(-2) = 6 + 4 = 10 which is what you wanted.