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equation 1) x - 2y = 1equation 2) x 2 + y 2 = 13 Rearrange equation 1 to: x = 1+2ysubstitute into equation 2: (1+2y) 2 + y 2 =13expand first bracket: (1+2y)(1+2y) +y 2 =13(1+4y+4y 2 ) +y 2 = 13Collect like t...

Equation 1) y=3x+4Equation 2) y=x+1 Rearrange equation 2 into terms of x as this is the simplest: x= y-1 (We do this by subtracting 1 off of each side to get X by itself)Substitute new equation 2 into 1: y=3...

X 2 - X -12 look at what numbers will add together and make 12. (2x6) or (3x4)Then see what of these combinations, when added together, makes -1. you have to consider that one of these values will be negativ...

The first thing to do, is see if it can be simplified: 5x -1 can't, however x^(3) - x simplifies to x(x^2 - 1) and then to x(x-1)(x+1) by the difference of two squares. So now we have (5x - 1)/(x(x-1)(x+1)) ...

Differentiation is a really common technique in a branch of maths called calculus. The idea is that you have a line on a graph (or a 'function') and we want to know the gradient - the steepness - of that cur...