The first three steps in determining the solution set of the system of equations algebraically are shown.

y = x2 − x − 3
y = −3x + 5

what are the solutions of this system of equations?

Since both are equivalent to y, the equations must be equivalent.
x^2-x-3= -3x+5
x^2+2x-8=0

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

Plug the values of x in to either equation
y=-3(-4)+5
y= 12+5
y=17

y= -3(2)+5
y=-6+5
y=-1

Final (-4,17) and (2,-1)