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Elza [17]
3 years ago
6

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

Mathematics
1 answer:
Nana76 [90]3 years ago
4 0
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
<u>- x              - x      </u>
  0 = -2x² + 5x - 3
  x = <u>-(5) +/- √((5)² - 4(-2)(-3))</u>
                        2(-2)
  x = <u>-5 +/- √(25 - 24)</u>
                   -4
  x = <u>-5 +/- √(1)
</u>              -4
  x = <u>-5 +/- 1</u>
             -4
  x = <u>-5 + 1</u>   or  x = <u>-5 - 1</u>
           -4                    -4
  x = <u>-4</u>              x = <u>-6</u>
        -4                    -4
  x = 1               x = 1.5

2y - 1 = x
2y - 1 = 1
<u>   + 1  + 1</u>
     <u>2y</u> = <u>2</u>
      2     2
       y = 1
 (x, y) = (1, 1)
or
2y - 1 = x
2y - 1 = 1.5
<u>    + 1 + 1    </u>
     <u>2y</u> = <u>2.5</u>
      2      2
       y = 1.25
 (x, y) = (1.5, 1.25)
The two solutions is equal to (1, 1) and (1.5, 1.25).
<u />
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