Expert: Lynn Houston - 12/5/2008

Question
We are trying to figure out how to do the following problem:

3x-5y=8
-2x+3y=3

Answer
There are at least 2 methods you can use.  One is to solve one eq for a variable and then insert that value into the second eq.  The other way is to multiply one or both eqs so that one variable has an equal (but opposite, one positive, one neg) value, then you add the two eqs.  I'll show you both (in the order listed).

3x-5y=8
x = (8+5y)/3  Now, insert the value of x into the next eq.

-2((8+5y)/3)+3y=3
(-16-10y)/3 + 3y = 3
-16-10y + 9y = 9
-y = 25
y = -25, therefore, x = -39

Or, multiply the first eq by 2 and the second by 3 to get

6x-10y = 16 and
-6x+9y = 9 Now, add the 2 equations
-y = 25, therefore x = -39.

You could have also multiplied the first eq by 3 and the second by 5 and solved for x.