## Simultaneous Equations With One a Quadratic

When solving ordinary – linear –simultaneous equations we multiply the equations by constant factorsto make the coefficient of some variable the same in magnitude, thenadd or subtract the equations to eliminate that variable.

For example, solve

(1)

(2)

(1)*2-(2)*3 eliminatestogive

Substitution of this value ofinto(1) to find a gives

If one of the equations is a quadratic wemay not be easily able to rearrange the equations to easily eliminateone of the variables and solve the equations. But we can rearrangeone of the equations – usually the linear one - to makeeitherorthesubject.

Example:

(1)

(2)

Rearrange (1) to makethesubject:andsubstitute this into (2) to get

To solve the last equation we can eitherfactorise or use the quadratic formula.

By factorising:or

IffromIffrom

By using the quadratic formula:

hence

or3.

As before , substitute these values ofbackinto (1) to obtain