Day 116 and 117 – March 1, 2

Algebra 1a: 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:

${\displaystyle 3x–y=9}$ and ${\displaystyle 2x+y=6}$

If we line them up, one under the other, we have:

${\displaystyle 3x–y=9}$

${\displaystyle 2x+y=6}$

Adding them together, we see that the sum looks like ${\displaystyle 3x+2x–y+y=9+6}$

or

${\displaystyle 5x=15}$

and solving for ${\displaystyle x}$ makes it ${\displaystyle x=3}$. If ${\displaystyle x=3}$, then we can plug it into EITHER original equation, I’ll use the second one and we can solve for ${\displaystyle y}$.

So…  ${\displaystyle 2x+y=6}$

becomes ${\displaystyle 2\cdot 3+y=6}$ or ${\displaystyle 6+y=6}$ or ${\displaystyle y=0}$. The ordered pair solution is then ${\displaystyle (3,0)}$!

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!