Find the point(s) of intersection of the parabola with equation y = x^2 - 5x + 4 and the line with equation y = 2x - 2

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At the point of intersection of the parabola y = x^2 - 5x + 4 and the line y = 2x - 2, the value of x and y is equal.

So we can equate the two and solve for x.

x^2 - 5x + 4 = 2x - 2

=> x^2 - 7x + 6 = 0

=> x^2 - 6x - x + 6 = 0

=> x(x-6) - 1(x - 6) = 0

=> (x - 1)(x -6) = 0

So we have x = 1 and 6

The value of y for x = 1 is 0 and for x = 6, y = 10.

Therefore the point of intersection are ( 1, 0) and (6, 10)

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Given the parabola y= x^2 - 5x + 4 and the line y= 2x-2

We need to find the intersection points of the parabola and the line.

The intersection points are the values of x and y such that:

the parabola y = the line y

==> x^2 - 5x + 4 = 2x -2

We will combine like terms and solve for x.

==> x^2 - 7x + 6 = 0

Now we will factor.

==> (x-6)(x-1) = 0

==> x1= 6  ==> y1= 2*6-2 = 10

==> x2 = 1==> y2= 2*1 -2 = 0

Then we have two intersection points:

The intersection points of the parabola and the line are (6, 10) and (1,0)

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