Sole the following system of equations 8x-3y=13 -3x-8y=-14

The system reads:

8x-3y=13

-3x-8y=-14

Solve this by solving for one variable at a time by cancelling the other.  We will begin by solving for y and cancelling x.  To do this, you need to find the least common multiple (LCM) of the x variables and multiply both equations by the number which will make them equal the LCM.  For 8 and 3, the LCM is 24, so you will multiply the top equation by 3 and the bottom one by 8.  

In order for the variables to cancel, the signs need to be opposite.  In this system, one is already positive and the other negative; if this were not the case, one of the equations would have needed to be multiplied by a negative number.

The system becomes:

24x-9y=39

-24x-24y=42

Now, you can combine the equations by adding them:

-33y=81

Solve for y:

*Divide both sides by -33*

y=27/11

To find x, you can select one of the given equations, plug in 27/11 for y, and solve for x.  We'll use the first equation:

8x-3(27/11)=13

8x-81/11=13

*Add 81/11 to both sides*

8x=224/11

*Divide both sides by 8*

x=28/11

Hope this helps!!

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