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Algebra 1 Notes Name: ____________________ Systems of Equations: Elimination Method Example 1: 5x − 6y = −32 3x + 6y = 48 1. If you add down, the y terms will eliminate themselves. 2. Now, we can solve for the x variable. 3. We will have to substitute the value we determined for x into one of the original equations to get the solution for the system. Combine the solved x value and the solved y value into an ordered pair to determine the solution for the system. ____________________. Example 2: 5x − 2y = 3 5x + y = −9 Try these: 1. € 2x − 5y = −20 4x + 5y = 14 2. 2y = 5 − 3x −5x + 2y = −7 Elimination with Multiplication Sometimes, the variables will not drop out by simply adding or subtracting. If the coefficients are different, we must ______________________ and then add or subtract to get the variables to drop out. Example 3: 2 x + 5 y = −22 10 x + 3 y = 22 Try These: A. 4m + 3n = 13 2m − 4n = 1 € B. 4x + 2y = 8 5x + 6y = 3 € Example 4: 4x + 2y = 14 7x − 3y = −8 In this problem we must multiply ______ equations by some number to make one of the variables drop out. Would x or y be would be easier? € Try this with a partner: C. 3x − 4y = 10 5x + 7y = 3 € Special Cases: 1. € 2x − y = −1 4x − 2y = 4 2. € −2 x + y = −1 3x −1.5y = 1.5