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 Question from mary, a student: solve the system by the method of substitution: -5x+2y=-15 4x-y=9

Hi Mary.

The "Substitution" occurs when you solve one of the equations for one of the variables, then use what it equals to substitute for the variable in the other equation.

For example:

2x + 3y - 9 = 2
6 - 2x = 2y

I can choose whatever I think will be easy to solve for. In this example, I will choose to solve the second equation for y.

6 - 2x = 2y becomes y = 3 - x.

Now I substitute (3 - x) into the first equation in place of every occurrence of y:

2x + 3y - 9 = 0 becomes 2x + 3(3-x) - 9 = 2

This has only one variable (x) in it, so I can solve for x now:

2x + 9 - 3x - 9 = 2
-x = 2
x = -2.

Now that I know x, I can choose either the first or second equation (whichever looks easier to me) and substitute -2 in for x:

6 - 2x = 2y becomes 6 - 2(-2) = 2y

This simplifies to

10 = 2y
y = 5.

Which solves my example: x = -2 and y = 5.

You can solve your problem exactly the same way, Mary.

Hope this helps,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.