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


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!)

Emily G. GCSE Physics tutor, A Level Geology tutor, GCSE Geography tu...

3 weeks ago

Answered by Emily, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Jonas P. IB Physics tutor, A Level Physics tutor, GCSE Physics tutor,...
View profile
£20 /hr

Jonas P.

Degree: MPhys Theoretical Physics (Bachelors) - Edinburgh University

Subjects offered: Maths, Physics


“I am currently a student at the University of Edinburgh, doing my 4th year of the MPhys Theoretical Physics programme. I've managed to score an average grade of 81% in year 3, and I tend to consistently do well in my exams, which I be...”

PremiumOsian S. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathemat...
View profile
£22 /hr

Osian S.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“Hi, I'm Osian, a Master's student at the University of Warwick. I've had fun with mathematics from a young age, and I hope to be able to instill this passion for mathematics in you, through my tutorials! Throughout my time at Warwick,...”

Tom H. A Level Economics tutor, A Level Maths tutor, A Level Spanish ...
View profile
£22 /hr

Tom H.

Degree: Economics (Bachelors) - Durham University

Subjects offered: Maths, Spanish+ 3 more

Business Studies

“Top tutor from Durham University, ready to help you improve your grades, all the way to A*.”

About the author

Emily G. GCSE Physics tutor, A Level Geology tutor, GCSE Geography tu...
View profile
£18 /hr

Emily G.

Degree: Geology (Masters) - Imperial College London University

Subjects offered: Maths, Physics+ 2 more


“Do you want help with Maths, Physics, Geology or Geography? Or desperately need a dedicated tutor to mentor you through writing your personal statement? Look no further! I’m Emily, studying Geology atImperial College London and wish t...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Calculate the largest share when £400 is shared in the ratio 1 : 2 : 5.

What are simultaneous equations and how do I solve them?

How do you find the equation of a straight line on a graph?

Can you explain the formula method for solving quadratic equations?

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss