SOLUTION: I need help with solving the system of equations algebraically. The problem is : y=2x^2 y= x+3

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Question 29299: I need help with solving the system of equations algebraically. The problem is : y=2x^2
y= x+3
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Try this:
y+=+2x%5E2 and y+=+x%2B3 Since y = y you can write:
2x%5E2+=+x%2B3 Simplify.
2x%5E2-x-3+=+0 Solve this quadratic by factoring.
%282x-3%29%28x%2B1%29+=+0 Apply the zero products principle.
2x-3+=+0 and/or x%2B1+=+0
If 2x-3+=+0 then 2x+=+3 and x+=+3%2F2
If x%2B1+=+0 then x+=+-1
We have found the x-coordinates of the solutions. To find the y-coordinates, substitute the x-values into either of the original equations and solve for y.
x+=+3%2F2 Substitute into y+=+x%2B3
y+=+3%2F2+%2B+3
y+=+3%2F2+%2B+6%2F2
y+=+9%2F2
x+=+-1 Substitute into y+=+2x%5E2
y+=+2%28-1%29%5E2
y+=+2
The solutions are:
(3/2, 9/2) and (-1, 2)
Why are there two solutions? Because you have a parabola y+=+2x%5E2 transversed by a line y+=+x%2B3
Here's a graph showing the two intersections/solutions.
graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C2x%5E2%2Cx%2B3%29