Solve the simultaneous equations (with a calculator)

x^2 + y^2 = 9

x + y = 2 

1) Firstly look at the second equation which is the simplest and think how you can rearrange it to fit into the first equation:

x + y = 2  can be rearranged to y = 2-x 

2) y = 2-x can then be substituted into the first equation, and 'gets rid of' the y in the process! Check it out:

x^2 + (2-x)^2 = 9 

3) now expand the brackets:

x^2 + (2-x)(2-x) = 9 

x^2 + 4 -2x -2x + x^2 = 9 

2x^2 -4x + 4 = 9 

4) Now if we can 'move the 9 over the equals sign', we will have an equation that equals zero.  This looks like a quadratic equation! 

2x^2 -4x - 5 = 0 

5) Always think 'factorise!' whenever presented with a  quadratic.  However this doesn't work in this case, so we are going to have to use the quadratic formula!

Try it and see! 

The answer is:

x = 2.87 and y = -0.87

or 

x = -0.87 and y = 2.87

TIP: always check your answer when you can (put the values back into the orignial equations

This question is a grade A* so don't worry if it seems difficult (I will be more than happy to go through simpler questions and then try and build up your  confidence from there!)

Answered by Emily G. Maths tutor

17036 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Expand the brackets in the following expression and indicate what the graph would look like: y=(5x+1)(2x-3)


Quadratic equation


Annie and Louis are going to the cinema with their friends. Annie buys two adult tickets and a popcorn for £18.Louis buys 4 adult tickets and 3 popcorn buckets for £45. How much is a ticket and a popcorn bucket?


In the isosceles triangle ABC, AB=AC and angle B=(3x +32)degrees and angle C=(87-2X)degrees


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences