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We have that y is inversely proportional to x, which we write mathematically as y ∝ 1/x. We need to be able to solve this, so we re-write this expression as an equations, y = k/x, where ...

Lets number the equations: 1) 3x + 2y = 17 2) 4x - y = 30If we double equation 2) we will get matching y coefficients so:8x - 2y = 60 if we rearrange this to be 8x-60 = 2y Then if we put these together: 3...

The chain rule is a technique used when differentiating. It is needed when differentiating composite functions, i.e. when y = f(g(x)).For example, y = sin(x^3) is a composite function, where (referring to...

1)Separating variables. Firstly, we need to get the y terms all on the dy/dx side and the x terms on the other side. In this case, we divide both sides by y which gives (1/y)dy/dx = 1/(x+...

The first aim is to obtain an expression for one of the unknowns in terms of the other. To achieve this, addition and subtraction methods are used. For example, using equation 1, subtracting 2y from both ...