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Solve the following system of equations. Show all work and solutions.

y = 2x^2 + 6x + 1
y = −4x^2 + 1

Answer :

  • y=2x²+6x+1
  • y=-4x²+1

Make the equations equal and solve for x

  • 2x²+6x+1=-4x²+1
  • 6x²+6x=0
  • 6x(x+1)=0
  • 6x=0 or x+1=0
  • x=0 or x=-1

For x=0

  • y=-4(0)+1=1

For x=-1

  • y=-4(1)+1=-3

The solutions are

  • (0,1) and (-1,-3)

Graph attached

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