SOLUTION: solve the following system by graphing and algebraically. y=1-x^2 4x^2+y^2=16

Question 572522: solve the following system by graphing and algebraically.
y=1-x^2
4x^2+y^2=16
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
ALGEBRAICALLY
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Substituting into ,
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The solutions to the above equation can be found by factoring
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does not yield a real solution for x in
results in --> and or
The solutions are (,-2) and (,-2).
GRAPHICALLY
I do not know if use of a graphing calculator is expected, but without it we could sketch, and then calculate to see if what looks like the intersection of the graphs really adds up.
graphs as a parabola with maximum at (0,1) and x-intercepts at x=-1 and x=1.
dividing both sides by 16 turns into .
That's the standard form of an ellipse centered at the origin, y intercepts (vertices) at y=-4 and y=4, and x-intercepts at x=-2 and x=2.
That would make us expect that the curves cross at negative values of y, with x between -2 and 2.
The graphs would look like this
If the graph suggested to you that the curves cross about at about y=-2, calculations would show you that y=-2 gives the same x value for both equations and you would have the solution.
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