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

Sagot :

Panoyinidn
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).
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