Solving by Elimination

You have now seen how to solve a linear system by graphing, it’s now time to see how it’s done algebraically.

Solving by graphing definitely has its limitations: it’s slow, takes up space, and not very accurate if you don’t have the right tools to graph or if the coefficient in front of the variables isn’t an integer.

The first technique that I’ll be showing you is called elimination, also known as the addition-subtraction method. Let’s watch a video on how it’s done:

  • Note that an arithmetic mistake was made at time 3:21. Bringing 1 over to the other side makes it 3 minus 1 = 2.

Sometimes you might get coefficients for x and y that are fractions, as is the case in the video below. When this occurs, you can still perform elimination the same way that was taught above, expect it’s best to first eliminate the fractions by finding a lowest common denominator to multiply the whole equation by.

SUMMARY – To solve a linear system by elimination, follow these steps:

1)   Arrange the two equations so that like terms are aligned.

2)   Choose the variable you wish to eliminate.

  • If necessary, multiply one or both equations by a value so that they have the same or opposite coefficient in front of the variable you want to eliminate.

3)   Add or subtract (as needed) to eliminate one variable.

4)   Solve for the remaining variable.

5)   Substitute into one of the original equations to find the value of the other variable.

6)   Check your solution by substituting into the original equations, or into the word problem.

7)   If you are solving a word problem, write the answer in words.