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y = x - 2

y² + x² = 10

1. Subsitutute the top equation into the second equation:

     (x-2)² + x² = 10

2. Exp...

Strictly speaking, the derivative is the rate of change of a function, process or pattern. 

So far, to calculate the gradient of a given function we always computed the change in the y coordi...

This is a typical example where the quotient rule is required to answer the question. This is clear because the function is made up of two other functions of x, one is the numerator and the other is the d...

a) We have that a₁ = 2 and a₄ = 14, so the first thing that we can conclude is that the common difference, d, is positive, and that a₂ and a₃ are in between 2 a...

[ 2x - 3y = 7 ] *3 = [ 6x - 9y = 21 ]

[ 3x + 4y = 2 ] *2 = [ 6x + 8y = 4 ]

[ 6x + 8y = 4 ] - [ 6x - 9y = 21 ] = [ 17y = -17 ] 

Therefore, y = -1.

Substituting y = -1 into the o...