This week we reviewed systems of equations and i re-learned how to do elimination and substitution because during those 3 weeks of break i mostly forgot how to do them.

Here is how you do elimination when using systems!

Say you have the problem…

x  + 2y = 12

x + 3y = 17

So the first thing you’ll want to do is make some zero pairs! So I’ll times the top equation by -1, to make the x’s cancel each other out.

-x – 2y = -12

x + 3y = 17

The x’s then cancel each other out so the equation is now…

-2y = -12

3y = 17

Then you add the equations and youll get…

y=5

You then must take the original equation once more and cancel the y’s out so that you get…

(x  + 2y = 12)-3

(x + 3y = 17)2

=

-3x – 6y = -36

2x + 6y = 34

The y’s then cancel each other out and it becomes…

-3x = -36

2x = 34

You then add them together and get…

(-x = -2)-1

=  x = 2 and y = 5

You can then verify your answer by putting it back into the original equation.

2  + 2(5) = 12 which is correct and therfore means the answer is right.

2 + 3(5) = 17 which is also correct and therfore means the answer is right.