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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
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:
6 - 3y = -6 ==> 6 - 6 - 3y = -6 - 6 ==> -3y = -12 ==> -3y / -3 = -12 / -3 ==> y = 4.
Therefore, the solution is x = 6, y = 4.
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