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!)