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