World 3-8Addition Method to Solve a System

Recall that a _______ of two linear equations can be solved by using let y1=y2 ie the

systemcomparison method ________________.

Consider the following system of equations.

6x + 4y = 14-6x +9y = 12

Instead of re-arranging to isolate y, simply add them up.

6x + 4y = 14-6x + 9y = 12

13y = 26 13 13 y = 2

sub y =2 to find x

6x + 4(2) = 14-8 -86x = 6 x = 1

-6x + 9(2) = 12-18 -18

-6x = -6 x = 1

(1, 2) is the solution

He offered her gifts and what happened??

He left the house because he was heartbroken …..

And went to the beach to cheer up

In some cases the system will need to be adjusted before a variable can be eliminated.Eg. 1

Step 2 Add the equations together to solve the unknown

3x + 4y = 19 2x - 5y = -18

Step 1 Multiply both equations so that one variable can be eliminated

x 2x -3

6x + 8y = 38-6x +15y = 54

23y = 92

23 23 y = 4

Step 3 Check answer by re-substituting the variable Into both equations

3x + 4(4) = 193x = 3 x = 1

2x -5(4) = -182x = 2 x = 1

(1, 4) is the solution

So he decided to get some exerciseHe wasn’t cheered up yet….

Eg. 2 Solve

x - 2y = -9 x + 3y = 16 x -1

x + -2y = -9 -x - 3y = -16

-5y

-5 -5

y = 5

= -25

Check sub y =5 to find x

x – 2y = -9 x – 2(5) = -9x – 10 = -9

x = 1

x + 3y = 16 x + 3(5) = 16

x = 1

(5, 1) is the solution

Eg. 3 Confidence Builder

x - 2y = -9 x + 3y = 16 x -1

x + -2y = -9 -x - 3y = -16

-5y

-5 -5

y = 5

= -25

Check sub y =5 to find x

x – 2y = -9 x – 2(5) = -9x – 10 = -9

x = 1

x + 3y = 16 x + 3(5) = 16

x = 1

(5, 1) is the solution

Will you be my Valentine?Ummm…….. I have to go fix my hair

Team Challenge Addition Method

1. Solve the System

2x + y = -4x - y = 4

2. Solve the System

3x + 4y = 24x + y = 7

3. Solve the System

2x + 8y = 8-2x + y = 10

4. Solve the System

x - 2y = 103x - y = 0

5. Solve the System

3x -4y = -155x -y = -15

After doing all of these things, he finallyrealized something…..

In trying to impress Ms. Relation, helearnt something newHow to solve a linear system!

Plus he realized they should just be friends…….For now.

Mini- Quiz

1. Find the POI between7x - y = 20 and y=x2 + x -12

2. Find the POI between3x + y +6 = 0 and y=2x2 - 7x + 4

3. Find the POI betweeny=x2 – 1 and x + y + 2 = 0