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!)

EG
Answered by Emily G. Maths tutor

18113 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

If we know that y is directly proportional to x and that when x=1, y=3, then what is the value of x when y=4?


How to use trigonometry to find angles or lengths


Solve the simultaneous equations y = 2x-3 and x^2 +y^2 = 2


What rules should I look out for when manipulating expressions?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning