Solving Quadratic Simultaneous Equations - like finding a tomato in your fruit bowl

Just when you feel like you’ve got simultaneous equations sorted they throw in a quadratic into the mix.

Remember algebra makes up a huge part of GCSE Maths and so if you struggle with expanding, factorising etc. you really need to work on that.

Improving your algebra is one of the fastest ways to improve your grade.

So let’s take a look at how to do simultaneous equations when one of them is a quadratic:

The basic method is this:

1: Rearrange the linear equation to get y =.

2: Substitute that into the quadratic equation

3: Rearrange the quadratic equation to make it equal zero.

4: Factorise and solve for x. There will be 2 solutions for x.

5: Substitute each value of x into one of the original equations to find the 2 values of y - the linear one will be easiest.

Let’s do an example - this is from the cgp maths textbook which you can grab from the shop.

Hope that helps!

Check back soon for more questions and examples!