Solve the simultaneous equations (with a calculator)

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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...

About the author

is an online GCSE Maths tutor with MyTutor studying at Imperial College London University

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