Thank you for the opportunity to help you with your question!

Our aim here is to eliminate one of the variables, either x or y, in order to solve for the other one. We can then substitute that value in and get the value of the other variable.

Let us label the equations as so:

x - 3y = -6 (1)

5x + 3y = 42 (2)

Notice that we have a negative 3y on the left hand side of equation (1) and a positive 3y on the left hand side of equation (2). Therefore, we can add the two equations together to eliminate y:

(1) + (2): x + 5x -3y + 3y = -6 + 42

Simplifying:

6x = 36

==> 6x / 6 = 36 / 6 ==> x = 6

We can now substitute this value of x into equation of the above equations to solve for y. Let us use equation (1) since the numbers are smaller and we don't have to multiply x by anything: