What

The first three steps in determining the solution set of the

system of equations algebraically are shown.

y=x²-x-3

y=-3x + 5

0000

Step

Equation

x²-x-3 = - 3x+5

0=x²+2x - 8

O = (x-2) (x+4)

2

I assume you want the equation to be solved, so this is a quadratic simultaneous equation.

y = x^2-x-3 - - - (1)

y = - 3x+5 - - - (2)

Sub (1) into (2)

(This is the first three steps provided)

x^2-x-3 = - 3x+5

0 = x^2+2x-8

0 = (x-2) (x+4) - - - (3)

Solve for x in (3):

x-2 = 0

x = 2

x+4 = 0

x = - 4

Sub x into (2)

y = - 3 (2) + 5

y = - 1

y = - 3 (-4) + 5

y = 17

Hence the solution sets are:

x=2, y=-1

x=-4, y=17