Help solving the linear system of equations

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Nov 3rd, 2015

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:

6 - 3y = -6  ==>  6 - 6 - 3y = -6 - 6  ==>  -3y = -12  ==>  -3y / -3 = -12 / -3  ==>  y = 4.

Therefore, the solution is x = 6, y = 4.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 3rd, 2015

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