Let's go back and look at the way we started that problem again:

10x + y = 35 and 4x - 7y = -23

What if we'd solved for this guy instead?

10x + y = 35 ... 4x - 7y = -23 ... 4x = 7y - 23 ... x = ( 7 / 4 )y - ( 23 / 4 ) ... stick that into the first equation... yuck!

10 ( ( 7 / 4 )y - ( 23 / 4 ) ) + y = 35

Oh, please...  Don't make me go on!

That thing got brutal fast!

So, if you can, always solve for a guy with no coefficient in front... 

Go for an x or -x or y or -y.

In my opinion, problems like this guy

3x + 8y = 2 and 2x - 7y = -11

Should be done with the method in the next section.
 


TRY IT:

Solve by substitution:

5x + 8y = 11 and x + 3y = -9