Ch 5.4 (part 2) Elimination Method (multiplying both equations) Objective: To solve a system of linear equations using multi-step elimination (multiplication and addition).

Rules Check Your Answers! Rearrange the equations so that “like” terms are lined up. Find the LCM (least common multiple) of the coefficients pertaining to one of the variables. Multiply one equation so the coefficient of the chosen variable equals the LCM Multiply one equation so the coefficient of the chosen variable equals the opposite of the LCM. Add the two equations to each other to eliminate a variable. 6) Solve for the remaining variable. Plug in the solution from step 6 into either equation and solve for the other variable. Check Your Answers! Plug in the x and y solutions into BOTH equations to verify that they both make TRUE statements.

Solve using elimination Example 1 Solve using elimination 3 ( ) 6x − 12y = 24 2x − 4y = 8 3x + 5y = 1 + -2 ( ) -6x − 10y = -2 -22y = 22 -22 -22 y = -1 2x − 4y = 8 2x − 4(-1) = 8 − 4 −4 2x = 4 x = 2, y = -1 x = 2

Solve using elimination Example 2 Solve using elimination 5 ( ) -10x + 15y = 25 -2x + 3y = 5 5x − 2y = 4 + 2 ( ) 10x − 4y = 8 11y = 33 11 11 y = 3 -2x + 3y = 5 -2x + 3(3) = 5 - 9 -9 -2x = -4 x = 2, y = 3 x = 2

Solve using elimination Example 3 Solve using elimination 3 ( ) -21x + 24y = -27 -7x + 8y = -9 3x − 5y = -4 + ( ) 7 21x − 35y = -28 -11y = -55 -11 -11 y = 5 -7x + 8y = -9 -7x + 8(5) = -9 - 40 -40 -7x = -49 x = 7, y = 5 x = 7

Classwork 5x + 2y = 4 9x + 5y = 10 -8x + 3y = 6 2x + 2y = -4 1) 5x + 2y = 4 2) 9x + 5y = 10 -8x + 3y = 6 2x + 2y = -4 3) -7x + 8y = -9 4) −3x − 6y = −12 3x – 5y = -4 7x − 12y = −24

-3x – 20y = -7 -9x – 8y = 1 -2x – 10y = -8 8x + 10y = 2 -7x – 9y = -7 5) -3x – 20y = -7 6) -9x – 8y = 1 -2x – 10y = -8 8x + 10y = 2 7) -7x – 9y = -7 8) 8x + 2y = 10 -4x + 7y = -4 6x + 5y = -3