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Solving Systems Involving Quadratic Equations

Solving Systems Involving Quadratic Equations. AII.5. Solving by Substitution. In Algebra 1 you learned to solve systems by substitution. As the title suggests, we will be ‘plugging in’ one equation into the other.

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Solving Systems Involving Quadratic Equations

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  1. Solving Systems Involving Quadratic Equations AII.5

  2. Solving by Substitution • In Algebra 1 you learned to solve systems by substitution. As the title suggests, we will be ‘plugging in’ one equation into the other. • Always solve the simpler equation for one of the variables and plug into the other equation. • You will have to use all your equation solving skills with this method…

  3. Solve: • Since both equations are solved for we can just set them equal to each other. • Solve for • Now find y by plugging back into one of the equations. • Solution:

  4. Solve: • Obviously the second equation is the less complex. Solve it for . Let’s be different and choose x this time. • => • Now replace in the first equation with • Now solve for

  5. Solve: Combine like terms Multiply out the binomials Combine like terms Since it is quadratic, set it equal to zero! Factor & Solve So = 5, 2; plug these into the other equation for

  6. Solve: • ; • (2 , ) (5, ) Solutions!!!

  7. Solve: • yand . Set them equal and solve for . So . Plug these values back into the first equation to find the corresponding -value. Solution: (0, 1), (3, 1), (-2, 1)

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