Lesson #28 – 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:

Lesson #28 – 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

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+15x= 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

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

Homework Weekend Assignment

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