Quadratic Aqa Higher

Quadratic simultaneous equations

What are quadratic simultaneous equations?

• When there are two unknowns (e.g. x and y) in a problem, we need two equations to be able to find them both; these are called simultaneous equations

• If there is an x² or y² or xy in one of the equations then they are quadratic (or non-linear) simultaneous equations

How do I solve quadratic simultaneous equations?

• Use substitution

  • Substitute the linear equation, y = … (or x = …), into the quadratic equation

    • Do not try to substitute the quadratic equation into the linear equation

• E.g. To solve and

  • Rearrange the linear equation into

  • Substitute this into the quadratic equation, replacing all y‘s with

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