ANSWER
The system has two solutions.
EXPLANATION
The given equations are
[tex]y=-2x + 2[/tex]
and
[tex]y={x}^{2} - 3x[/tex]
We equate both equations to obtain;
[tex] {x}^{2} - 3x =-2x + 2[/tex]
This implies that,
[tex] {x}^{2} - 3x +2x - 2 = 0[/tex]
[tex] {x}^{2} - x - 2 = 0[/tex]
where a=1, b=-1,c=-2.
We find the discriminant, D=b²-4ac of this equation to be;
[tex]D = {(-1)}^{2} - 4(1)( - 2) = 9[/tex]
Since the discriminant is greater than zero, it means the two functions intersected at two distinct points.
Hence the system has two solutions.
