# 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!

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!)

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