Hi Patricia.

To figure out what to eliminate, I look at the pairs of monomials and try to see if there is an easy factor I can apply so that one is the negative of the other. We have 5/x and 25/x for one pair and 3/y and -2/y for the other pair. Right away, I can see that it is easy to change the 5/x into -25/x by multiplying by -5. Then I have a pair that consists of the same number with opposite signs.

So I'll first multiply the top equation by negative five.

5/x + 3/y=4 becomes -25/x - 15/y = -20.

Next, add the equations. Add the two right sides together and the two left sides together:

(-25/x - 15/y) + (25/x - 2/y) = -20 + 3.

This reduces to:

-17/y = -17.

You see how I eliminated the x term?

Hope this helps you,
Stephen La Rocque.