World 3-8 Addition Method to Solve a System. Recall that a _______ of two linear equations can be solved by using let y 1 =y 2 ie the system comparison.

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Presentation transcript:

World 3-8 Addition Method to Solve a System

Recall that a _______ of two linear equations can be solved by using let y 1 =y 2 ie the system comparison 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= y = 2 sub y =2 to find x 6x + 4(2) = x = 6 x = 1 -6x + 9(2) = x = -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 2 x -3 6x + 8y = 38 -6x+15y= 54 23y = y = 4 Step 3 Check answer by re-substituting the variable Into both equations 3x + 4(4) = 19 3x = 3 x = 1 2x -5(4) = -18 2x = 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 = y -5 y = 5 = -25 Check sub y =5 to find x x – 2y = -9 x – 2(5) = -9 x – 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 = y -5 y = 5 = -25 Check sub y =5 to find x x – 2y = -9 x – 2(5) = -9 x – 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 = -4 x - y = 4

2. Solve the System 3x + 4y = 24 x + y = 7

3. Solve the System 2x + 8y = 8 -2x + y = 10

4. Solve the System x - 2y = 10 3x - y = 0

5. Solve the System 3x -4y = -15 5x -y = -15

After doing all of these things, he finally realized something….. In trying to impress Ms. Relation, he learnt something new How to solve a linear system! Plus he realized they should just be friends……. For now.

Mini- Quiz 1.Find the POI between 7x - y = 20 and y=x 2 + x Find the POI between 3x + y +6 = 0 and y=2x 2 - 7x Find the POI between y=x 2 – 1 and x + y + 2 = 0