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

17040 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do you calculate ratios? Example question: 'White paint costs £2.80 per litre, Blue paint costs £3.50 per litre, White paint and blue paint are mixed in the ratio 3:2. Work out the cost of 18 litres of the mixture [4 marks]' AQA Mathematics (8300)


Two simultaneous questions are given as 3x+2y = 9, and x-2y = -5. Find the values for x and y


In integration, what does the +c mean and why does it disappear if you have limits?


Solve the Simultaneous equations. 3x+5y=22 4x-5y=6


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