Question

Y = 2x - 1
y = x² - 2x + 2

Answer 1

x = 1, x = 3 are the solutions

Explanation:

Since the left side of both equations is y we can set the right sides equal to each other and solve:

x² - 2x + 2 = 2x - 1

Subtract 2x from both sides:
x² -2x - 2x + 2 = 2x - 2x - 1

x² - 4x + 2 = -1

Add 1 to both sides

x² - 4x + 2 + 1 = -1 + 1

x² - 4x + 3 = 0

We can factor the left side expression as follows:
x² - 4x + 3 = (x - 1)(x -3)

which gives

(x - 1)(x -3) = 0

This means either x - 1 = 0 giving a solution of x = 1

or

x - 3 = 0 giving a solution of x =3