Linear combination
- 1. ACT OpenerACT Opener Solve each system by substitution. 1) 2) 3) 4)
- 2. Solve System bySolve System by Linear Combination MethodLinear Combination Method 1. Determine which variable to eliminate. 2. Determine by what number to multiply each equation. 3. Multiply each equation. 4. Determine whether to add or subtract, then do it. – Add if the coefficients are opposites. – Subtract if the coefficients are the same. 1. Substitute to find the other term.
- 3. Linear Combination MethodLinear Combination Method • This method is also known as – Elimination – Add/Subtract Method
- 4. Example 1Example 1 x – y = 7 x + y = 3 2x + 0y = 10 2x = 10 x = 5 x + y = 3 5 + y = 3 y = -2 (5,-2) Solve using the addition method.
- 5. Example 2Example 2 2x + 3y = 11 -2x + 9y = 1 0x + 12y = 12 12y = 12 y = 1 2x + 3y = 11 2x + 3(1) = 11 2x + 3 = 11 2x = 8 x = 4 (4,1) Solve using the addition method.
- 6. PracticePractice 1) Solve using the addition method. x y 5 2x y 4 + = − = 2) 3x 3y 6 3x 3y 0 − = + =
- 7. Example 3Example 3 Solve using the addition method. 3x – y = 8 x + 2y = 5 x + 2y = 5 3x – y = 8 multiply as needed(-3)( ) ( )(-3) 3x – y = 8 -3x – 6y = -15 addition property -7y = -7 y = 1 3x - (1) = 8 3x = 9 x = 3 (3,1)
- 8. Example 4Example 4 8x 2y 10 4x 15 3y + = − = + 4x – 3y = 15 write in standard form8x + 2y = -10 multiply as needed(-2)( ) ( )(-2) 8x + 2y = -10 -8x + 6y = -30 addition property 8y = -40 y = -5 8x + 2(-5) = -10 8x - 10 = -10 8x = 0 x = 0 (0,-5) Solve using the addition method.
- 9. PracticePractice 1) Solve using the addition method. 5x 3y 17 5x 2y 3 + = − = − 2) 8x 11y 37 11y 7 2x + = − =
- 10. PracticePractice 1) Solve using the addition method. 5x 3y 17 5x 2y 3 + = − = − 2) 8x 11y 37 11y 7 2x + = − =