Substitution Method                    Page 3 of 5

Example 2

​Here's a system that's a little bit harder: 2x + y = 11 and y = 3x - 9

It's not as simple as the first example because there's no easy x = some number that you can plug into the other equation. Let's pretend though that it had said y = 5 for the second equation. What would you do? You would plug in 5 for y into the first equation. Instead of just having y = some number, we have y = 3x - 9. No worries, we'll just plug the whole thing in! Take out the y in the first equation and replace it with 3x - 9:

​A common mistake is for students to stop here and write x = 4 as the answer.  Remember, the solution to a system is an ordered pair. We need both the x and the y to write the solution.  We've just found half of the answer by finding that x = 4.

​How do we find the y-coordinate? We can go back to the original system and plug in 4 for x into either equation. It does not matter which equation you choose - pick the one that looks easiest to you. We'll pick the second equation since that has a y by itself.

We could check our answer by graphing the two lines to see if they cross at the point (4,3).  A faster way to check your answer is to go back to the other original equation (the one that you didn't use to find y) and plug in the values for x and y.  If you use the same equation twice, it won't catch a mistake.

Check:

​To sum it up, here are the steps that you can use when solving a system of equations with the substitution method:

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