How to Solve Simultaneous Quadratic Equations

Two separate quadratic equations may be presented simultaneously so as to be used to solve each other. These tandem equations have a synergistic relationship since they would be unsolvable if attempted individually. Simultaneous quadratic equations are important tools in both practical and linear algebra, and solving them relies on basic algebraic procedures and simple substitution methods.

Instructions

    • 1

      Pick the equation with a lesser exponential power to begin working with. If you have an equation which is

      x+y=2

      and the other one is

      x^2+2y=12,

      then chose the first equation.

    • 2

      Solve the equation for a variable. Work the equation

      x+y=2

      to find the value of one variable in relation to the other. Solve this equation for y, so

      y=x-2.

    • 3

      Substitute the value of y into the other equation. The equation

      x^2+2y=12

      will be rewritten as

      x^2+2(2-x)=12.

    • 4

      Multiply out the terms and put the equation into quadratic form.

      x^2+2(2-x)=12

      becomes

      x^2+4-4x=12.

      Rearranging the terms, the equation becomes

      x^2-2x-8=0.

    • 5

      Solve the equation for the variable.

      x^2-2x-8=0

      becomes

      (x-4)(x+2)=0.

      x equals -2 and 4.

    • 6

      Substitute the values into the first equation. So

      -2+y=2 and 4+y=2

      and y equals -2 and 4.

Learnify Hub © www.0685.com All Rights Reserved