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Say you are given the equations of both a line and a curve, for example y=x²+8x-1 and y=3x-7, and asked to find where these two intersect. This just means w...

Label the equations (1): 2x + 3y = 4 (2): 3x + 6y = 3We need the same number of x's or y's in the equations, so multiply (1) by 3 and (2) by 2 giving (3): 6x + 9y = 12 (4): 6x + 12y = 6Subtract (3) from (...

We need two numbers, a and b, such that a*b = 2 and a+b=3Looking at the equation it can be seen that 2 and 1 fulfill these conditions.Therefore x² +3x +2=0        = (x+2)(x+1)=0This means we ne...

Often quadratic equations of the form ax²+bx+c=0 can be easily solved by factorising. First, find pairs of numbers that multiply t...

f(c) means let x=c. Remember that c is just an unknown number.

The expression f(c)=9 means that when we put c through the function f(x)=7-4x, it gives the answer 9. Therefore we know 7-4c...