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!!
