How would solve system y=2x-1 , y=x^2-3x+5?

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The system of equations y=2x-1 , y=x^2-3x+5 has to be solved.

2x - 1 = x^2 - 3x + 5

=> x^2 - 5x + 6 = 0

=> x^2 - 3x - 2x + 6 = 0

=> x(x - 3) - 2(x - 3) = 0

=> (x - 2)(x - 3) = 0

=> x = 2 and x = 3

For x = 2, y = 3 and for x = 3, y = 5

The solution of the given set of equations is (2, 3), (3, 5)

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