1. Dr. Fowler CCM Solving Systems of Equations By Elimination – Harder

2. Solving a system of equations by elimination using addition and subtraction. Step 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Step 3: Add or subtract the equations. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Standard Form: Ax + By = C Look for variables that have the same coefficient. Solve for the variable. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations. ALREADY IN NOTES – Read Only for Review

3. Elimination using Multiplication 1) Solve the system. Adding or subtracting will not eliminate x + 2y = 6 3x + 3y = -6 But, we can multiply the first equation by -3 to eliminate the x term

4. Elimination using Multiplication x + 2y = 6 3x + 3y = -6 -3 ( ) 1) Solve the system.

5. Elimination using Multiplication -3x + -6y = -18 3x + 3y = -6 + -3y = -24 y = 8 ANS: (x, 8)  Be sure to distribute the -3 to ALL in the equation. 1) Solve the system.

6. Elimination using Multiplication x + 2y = 6 3x + 3y = -6 ANS: (x, 8) Substitute y = 8 into equation y =8 x + 2(8) = 6 x + 16 = 6 x = -10  1) Solve the system.

7. Elimination using Multiplication x + 2y = 6 3x + 3y = -6 Answer: ( -10, 8) Substitute y = 8 into equation y =8 x + 2(8) = 6 x + 16 = 6 x = -10  1) Solve the system.

8. 2) Solve the system: 2(2) + 2y = 6 4 + 2y = 6 2y = 2 y = 1 2x + 2y = 6 3x – y = 5 If we multiply the bottom equation by 2 we can eliminate y: 2x + 2y = 6 (2)(3x – y = 5) 2x + 2y = 6 (+) 6x – 2y = 10 8x = 16 x = 2 (2, 1) Substitute x = 2 into either original equation:

9. More complex Problems 3x + 4y = -25 2x - 3y = 6 Multiply by 2 Multiply by -3. This will get X’s to MATCH 3) Solve the system

10. More complex Problems 3x + 4y = -25 2x - 3y = 6 2( ) -3( ) 3) Solve the system

11. More complex Problems 6x + 8y = -50 -6x + 9y = -18 + 17y = -68 y = -4 Answer: (x, -4)  3) Solve the system

12. More complex Problems 3x + 4y = -25 2x - 3y = 6Substitute y = -4 2x - 3(-4) = 6 2x - -12 = 6 2x + 12 = 6 2x = -6 x = -3  Answer: (-3, -4) 3) Solve the system

13. 3x + 4y = -1 4x – 3y = 7 4) Solve the system using elimination. 3(1) + 4y = -1 3 + 4y = -1 4y = -4 y = -1 Multiply both equations (3)(3x + 4y = -1) (4)(4x – 3y = 7) 9x + 12y = -3 (+) 16x – 12y = 28 25x = 25 x = 1 (1, -1)

14. Excellent Job !!! Well Done

15. Stop Notes Do Worksheet