   SEARCH HOME Math Central Quandaries & Queries  Subject: the substitution method Name: victoria Who are you: Student how do i solve this problem using the substitution method? 2x-5= -14 -7x+14y= -5 Hi Victoria.

With the substitution method, you solve one equation (whichever is easier) for one variable (whichever is easier). Then you can substitute that expression for the variable in the second equation and solve for the other variable.

Here's an example: 2x - 9y = 10 and y - 2x = -5

It looks like the second is easy to solve for y, so I choose that.

y - 2x = -5 becomes y = 2x - 5.

That's what y equals. If y equals that, then we can substitute what y equals for the letter y in the first equation.

So 2x - 9y = 10 becomes 2x - 9(2x - 5) = 10

and this becomes:

2x - 18x + 45 = 10
-16x = -35
x = 35/16

Now we have a value for x, we substitute that into either one (whichever is easier) of the original equations and find y.

So y - 2x = -5 becomes y - 2(35/16) = -5

and this becomes:

y - 35/8 = -5
y = -5 + 35/8
y = -5/8

We can check our work by seeing if x = 35/16 and y = -5/8 works for the other equation:

2x - 9y ?=? 10
2(35/16) - 9(-5/8) ?=? 10
35/8 + 45/8 ?=? 10
80/8 ?=? 10
10 = 10.
it checks.

Now you try it.
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.