# AS level Maths (pure) - HELP ME wtf is this question

So, doing non linear simultaneous equations, if anyone can offer some step by step help that would be really appreciated,

The question is to simultaneously solve: (^2 = squared)

x^2 +8y=13
x+2y=2

I know what the answer is but how do i get there? ( Answer is:

x=-1
x=5
y=3/2
y=-3/2

Please can you help me with the method (Preferably in the simplest way using substitution method) Thank you y'all are angels...if you help me lol
It basically just/similar to a line intersecting a circle/parabola (so you did this at gcse) so get 8y from the second equation in terms of x and substitute into the first and solve the quadratic to get x's, then ...
(edited 3 weeks ago)
Make the second equation equal to x so x=2-2y then substitute this into the quadratic so (2-2y)^2+8y=13 solve that quadratic normally to find the y values then substitute those into x=2-2y to find your 2 X values.
Original post by mkr_08
Make the second equation equal to x so x=2-2y then substitute this into the quadratic so (2-2y)^2+8y=13 solve that quadratic normally to find the y values then substitute those into x=2-2y to find your 2 X values.

might be easier to work out 2y in terms of x instead tbf, so 2y = 2-x, and then replacing 8y with 4(2-x), to get a quad with x to solve.
Original post by jobajojoba
might be easier to work out 2y in terms of x instead tbf, so 2y = 2-x, and then replacing 8y with 4(2-x), to get a quad with x to solve.

Thank u so much, finally got that hang! @mqb2766 thank u too, you helped me along with the basicalities of the question, you're both angels xxx