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Sample Point Of Intersection Calculation: Quadratic With Line

Find the points of intersection algebraically of the graphs of the equations

y=x^2-3x+4, and 2x-2y= -8

need to see the algebra got a bit lost as to how to get from

Solve equations:
Take y=x^2-3x+4 into 2x-2y=-8, we got: Here

x-x^2+3x-4=-4 to here
We got: x1=0, x2=4
Then we got y1=4, y2=8