1. Lesson #28 – Addition Method to Solve a System

2. 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= 26 13 y = 2 sub y =2 to find x 6x + 4(2) = 14 -8 6x = 6 x = 1 -6x + 9(2) = 12 -18 -6x = -6 x = 1 (1, 2) is the solution

3. 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 = 92 23 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

4. Eg. 2 Solve x - 2y = -9 x + 3y = 16 x -1 x + -2y = -9 -x - 3y = -16 -5y -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

5. Eg. 3 Confidence Builder x - 2y = -9 x + 3y = 16 x -1 x + -2y = -9 -x - 3y = -16 -5y -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

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

7. Team Challenge Addition Method

8. 1. Solve the System 2x + y = -4 x - y = 4

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

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

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

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

13. Homework Weekend Assignment

14. Mini- Quiz 1.Find the POI between 7x - y = 20 and y=x 2 + x -12 2. Find the POI between 3x + y +6 = 0 and y=2x 2 - 7x + 4 3. Find the POI between y=x 2 – 1 and x + y + 2 = 0