SOLUTION: My question is in reference to one involving "Solving systems of linear equations by the Addition method". I am asked to solve a system of two linear equations in two variables by

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Question 263034: My question is in reference to one involving "Solving systems of linear equations by the Addition method". I am asked to solve a system of two linear equations in two variables by the addition method. Here are the equations, I need to solve for both X and Y.
5x/6+y/3=4/3 and
2x/3-y/2=11/6
I have tried using by multiplying by 6 and got
5x+2y=8 and 4x-3y=11
9x-y=19
I know this is not the answer so I am unsure what to do.
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Well, your fist step simplified the two equations by clearing the fractions and that was a good move!
You ended up with:
1) and...
2) but simply adding these doesn't do you much good unless you eliminate one of the two variables in the process.
So the idea is to multiply one or both equations by a number that will result in having identical (or opposite in this case) coefficients for either variable so that when you add the two, per instructions, you will eliminate one of the variables.
So, looking at the two equations you got when you multiplied through by 6, you can make the coefficient of y equal to 6 and -6 respectively by multiplying equation 1) by 3 and equation 2) by 2.

1a) and...

2a) Now when you add equations 1a) and 2a), you will eliminate the y variable.

Add these.
-----------------
Divide both sides by 23.
Now substitute this into either one of the two equations 1) or 2) to solve for y.
I'll leave this for you to finish up!