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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.