Question

Solve the simultaneous equations
y=x²-x-13
y=x+2

Answer 1

`{x}^(2) - x - 1 = x + 2 \\ {x }^(2) - x - 1 - x - 2 = 0 \\ {x}^(2) - x - x - 1 - 2 = 0 \\ {x}^(2) - 2x - 3 = 0 \\ (x - 3)(x + 1) = 0 \\ x - 3 = 0 \\ \\ or \\ x + 1 = 0 \\ \\ x = 3 \\ \\ or \\ \\ x = - 1`

WHEN x=3

`y = 3 + 2 \\ y = 5`

When x=-1

`y = - 1 + 2 \\ y = 1`

NOW WE HAVE A PAIR OF SOLUTIONS AS

(3,5) and (-1,1)