Question

Solve using the elimination method...

11x + 10y = 147

0x + 2y = 14

Answer 1

\[11x+10y=147\]
\[0x+2y=14\]

What you want to look for is a way to make the coefficients of either x or y the same (in absolute value). That way when you add or subtract the two equations, you will get a coefficient of 0 for that variable, which will allow you to solve for the other variable. The best way to do start is to find a variable where the coefficient in one equation is the multiple of another. In this case, 2-> one of the coefficients of y, multiplied by 5 = 10, the other coefficient of y.

In order to keep the second equation true, you need to multiply both sides of the equation by 5. So the second equation becomes
\[0x*5+2y*5=14*5\]
OR
\[0x+10y=70\]

Subtracting the second equation from the first, you get 11x+0y=77
solving for x, x=77/11, so x=7, and plugging back into the original equation (or really just solving the second equation for y), you find that y is 7 also.

[Hmmm, bizarre, is anyone else getting this answer?]