# Simultaneous equations with one linear and one quadratic - Higher

A does not contain any powers higher than 1. A contains a variable that's highest power is 2. For example:

is a linear equation and is a quadratic equation.

## Solving simultaneous equations with one linear and one quadratic

Algebraic skills of substitution and factorising are required to solve these equations.

When solving simultaneous equations with a linear and quadratic equation, there will usually be two pairs of answers.

Substitute into the quadratic equation to create an equation which can be factorised and solved.

Substitute :

Rearrange the equation to get all terms on one side, so subtract and from both sides:

Factorise this equation:

If the product of two numbers is zero, then one or both numbers must also be equal to zero. To solve, put each bracket equal to zero.

To find the values for , substitute the two values for into the original linear equation.

when

when

The answers are now in pairs: when , and when ,