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Systems of Equations

Systems of Equations. Elimination. Elimination. This method is a little harder than substitution because you have to think a bit! In elimination, you will be “eliminating” a variable to solve the problems.

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Systems of Equations

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  1. Systems of Equations Elimination

  2. Elimination • This method is a little harder than substitution because you have to think a bit! • In elimination, you will be “eliminating” a variable to solve the problems. • Which variable is determined by what the problem looks like or what you feel like getting rid of first.

  3. Elimination • Solve using elimination: • 2x – y = 5 • -x + y = - 2 2x – y = 5 -x + y = - 2 x = 3 2(3) – y = 5 6 – y = 5 - y = - 1 y = 1 (3, 1) Add the equations together to get rid of a variable. Plug the variable back into one of the equations to get the other variable.

  4. Elimination • That was an easy one. Sometimes you have to multiply to get rid of a variable. 2x – y = -6 4x - y = 6 (2x – y = -6) -1 - 2x + y = 6 4x – y = 6 2x = 12 x = 6 2(6) – y = - 6 12 – y = - 6 - y = - 18 y = 18 (6, 18) You have to multiply one equation to get rid of a variable. Add the two equations and then solve for the variable. Plug the variable back in and solve for the other variable.

  5. Elimination • 2x – 3y = 9 4x – 4y = 2 (2x – 3y = 9) -2 -4x + 6y = -18 4x – 4y = 2 2y = - 16 y = - 8 2x – 3(-8) = 9 2x + 24 = 9 2x = -15 x = -15/2 (-15/2, -8)

  6. Elimination • Try a couple on your own! 2x + 3y = 1 x – 5y = 2 x – y = 14 4x – 3y = -7 -10x + 50y = -20 -x + y = 9 (-1, 1) Infinitely Many No Solution

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