Graph the system of equations:

y=-x^2+3x-1

2y-1=x

Y = - x² + 3x - 1

x = 2y - 1

x = 2 (-x² + 3x - 1) - 1

x = 2 (-x²) + 2 (3x) + 2 (-1) - 1

x = - 2x² + 6x - 2 - 1

x = - 2x² + 6x - 3

- x - x

0 = - 2x² + 5x - 3

x = - (5) + / - √ ((5) ² - 4 (-2) (-3))

2 (-2)

x = - 5 + / - √ (25 - 24)

-4

x = - 5 + / - √ (1)

-4

x = - 5 + / - 1

-4

x = - 5 + 1 or x = - 5 - 1

-4 - 4

x = - 4 x = - 6

-4 - 4

x = 1 x = 1.5

2y - 1 = x

2y - 1 = 1

+ 1 + 1

2y = 2

2 2

y = 1

(x, y) = (1, 1)

or

2y - 1 = x

2y - 1 = 1.5

+ 1 + 1

2y = 2.5

2 2

y = 1.25

(x, y) = (1.5, 1.25)

The two solutions is equal to (1, 1) and (1.5, 1.25).