Solving Quadratics by Substitution

1
Solving Quadratics by Substitution
y2 x 6 0 x y 0
Solve for x or y Plug in the expression for y.
y -x (-x)2 x 6 0 x2 x 6 0 (x
2)(x 3) 0 x -2 x 3
Simplify and combine like terms
Solve the Quadratic by factoring.(If you cant
factor use quadratic formula or completing the
square)
y - (-2) y -(3) y 2
y -3
Plug your answers back into one of the original
problems.
(-2,2) (3,-3)
Solutions are point of intersection.
2
Solving Quadratics by Substitution
y x2 2x 3 y -x2 2x 3
Solve for x or y Since they are both already y
you can set them to each other.
x2 2x 3 -x2 2x 3 2x2 4x 6 0 x2
2x - 3 0 (x 1)(x 3) 0 x 1 x -3
Simplify and combine like terms
Solve the Quadratic by factoring.(In this problem
you can divivide by 2 first)
Plug your answers back into one of the original
problems.
y 12 2(1) 3 y (-3)2 2(-3) 3 y
1 2 - 3 y 9 6 3 y 0
y 0
Solutions are point of intersection.
(1,0) (-3,0)
3
Solving Quadratics by Substitution
x2 6x 4y 3 0 y 3x 1 0
Solve for x or y Plug in the expression for y.
Simplify and combine like terms
Solve the Quadratic by factoring.(If you cant
factor use quadratic formula or completing the
square)
Plug your answers back into one of the original
problems.
Solutions are point of intersection.
4
Practice Problems