Simultaneous Quadratic Equations

Maths: Edexcel A Level Pure Maths, topic 2.5.3

Nonlinear Systems of Equations

Find the solutions to the following sytem of equations 2x² + y = 5 and 2x + y = 1:

Label the equations

Label the equations

Rearrange the non quadratic equation

Rearrange the non quadratic equation

Substitute the rearranged equation into the quadratic

Substitute the rearranged equation into the quadratic

We get this

We get this

Expand any parentheses

Expand any parentheses

Rearrange in the form ax² + bx + c 0

Rearrange in the form ax² + bx + c = 0

Factorize

Factorize

Find solutions for x

Find solutions for x

Look at our earlier equation for y

Look at our earlier equation for y

Sub in our first solution for x

Sub in our first solution for x

We get this

We get this

Solve to get our first solution for y

Solve to get our first solution for y

Sub in our second solution for x

Sub in our second solution for x

We get this

We get this

Solve to find our second solution for y

Solve to find our second solution for y

These are the solutions

These are the solutions

Remember, each y solution matches to each x solution.
x = 2, y = 3 is NOT a solution!

Test yourself on Simultaneous Quadratic Equations

If a = 6 and a+b=12, what is b?

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