Question

Graph the system of equations:
y=-x^2+3x-1
2y-1=x

Answer 1

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).