How to Solve a System of Equations with a Parabola and Ellipse?

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Homework Help Overview

The discussion revolves around solving a system of equations involving a parabola and an ellipse, specifically the equations y = 5x^2 + 1 and x^2 + 6y^2 = 21.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to solve the equations algebraically and seeks guidance on manipulating the formulas to find intersection points. Some participants suggest methods for substitution and rearranging equations to facilitate solving for y and x values.

Discussion Status

Participants are exploring different approaches to solve the problem, with some offering algebraic manipulation techniques. There is no explicit consensus on a single method, and the discussion remains open with various interpretations being considered.

Contextual Notes

The original poster provides specific values for the parabola and ellipse but does not indicate whether these points are intended to be solutions or examples. There may be constraints related to the homework guidelines that influence the discussion.

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Homework Statement



y = 5x^2 + 1
x^2 + 6y2 = 21


Homework Equations



quadratic formula

The Attempt at a Solution



I am not quite sure how to solve algebraically...
My parabola is this
x|y
0 1
1 6

ellipse
x|y
0 | 1.87
4.5 | 0

How can I manipulate the formula to solve the points which the ellipse crosses the parabola
 
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Try solvng for x^2 and plugging that into one equation. Then plug in each y solution to get 2 corresponding x solutions. At the end, check to make sure all your answers work in the original equations
 
Not sure what you mean... =/
 
Rearrange your second equation to give [itex]x^2=21-6y^2[/itex], then substitute this into the first equation [itex]y=5x^2+1[/itex]. You will obtain a quadratic equation in y which you should be able to solve.
 

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