Algebra: Chapter 8, Lesson 3, page 367.
Addition and Subtraction for 2 linear equations.
You can add 2 (or subtract) linear equations together so that one of the variables cancels out. An example would be:
`3x – y = 9` and `2x + y = 6`
If we line them up, one under the other, we have:
`3x – y = 9`
`2x + y = 6`
Adding them together, we see that the sum looks like `3x + 2x – y + y = 9 + 6`
or
`5x = 15`
and solving for `x` makes it `x = 3`. If `x = 3`, then we can plug it into EITHER original equation, I’ll use the second one and we can solve for `y`.
So… `2x + y = 6`
becomes `2*3 + y = 6` or `6 + y = 6` or `y = 0`. The ordered pair solution is then `(3, 0)`!
We may sometimes have to scale (multiply) ONE OR BOTH of the equations to make one of the variables disappear. Here is a link that can help!