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!
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 3 Review
Skills Practice 8 and 9
A good overview of Chapter 3 prior to our Benchmark #1, covering Chapters 1 through 3, on Friday! Make sure that your notes are up-to-date.
Remember how to do the whickity-whack divide thingy.
Remember the steps to SOLVING 2-STEP EQUATIONS:
- Multiply both sides to clear fractions or decimals, if necessary.
- Collect like terms on each side, if necessary.
- Use the addition property to move the variable to one side and all other terms to the other side of the equation.
- Collect like terms again, if necessary
- Add or subtract to isolate the variable and finally
- Use the multiplication or division or reciprocal properties to solve for the variable.