How many solutions does the system have?

{y=−2x+2
{y=x^2−3x

enter your answer in the box

If a solution(s) exists y=y so we can say:

x^2-3x=-2x+2  add 2x to both sides

x^2-x=2  subtract 2 from both sides

x^2-x-2=0  factor

(x-2)(x+1)=0

So x=-1 and 2, using y=-2x+2 we find:

y(-1)=4 and y(2)=-2

So the two solutions occur at the points:

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