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There are 2 methods of solving this: completing the square or calculus, which makes this a versatile question for both GCSE and A Level students. It is also fairly simple to adapt.
Using calculus, th...

First rearrange x - 2y = -3 by adding 2y to each side to give x = -3 + 2ySubstitute this into the first eq. to give 3(-3 +2y) + y = 19Expand brackets first: -9 + 6y + y = 19Rearrange and simplify by colle...

dy/dx = 4/(x^2+5) - 4x(2x)/(x^2+5)dy/dx= 4(5-x^2)/(x^2+5)^2Part B4(5-x^2)/(x^2+5)^2<05-x^2<05<x^2

First we need to use the factor theorem to find a factor.f(1)=-25 so x-1 is not a factorf(-1)=9 so x+1 is not a factorf(2)=0 so x-2 is a factorSo x-2 is our starting point, we need to polynomial division ...

To solve these equations you first want to eliminate the same variable from each equation. In this question it is easiest to eliminate Y, to do this we will times equation 1 by 3 to get 21X-18Y=114 and eq...