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

In summary, the conversation was about solving the system of equations y = 5x^2 + 1 and x^2 + 6y^2 = 21 using the quadratic formula. The solution involved manipulating the equations to obtain a quadratic equation in y, which can be solved to find the points where the ellipse and parabola intersect.
  • #1
duki
264
0

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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  • #2
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
 
  • #3
Not sure what you mean... =/
 
  • #4
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.
 

1. What is a system of equations?

A system of equations is a set of two or more equations that contain multiple variables. The solution to a system of equations is the set of values for each variable that makes all of the equations true simultaneously.

2. How can I solve a system of equations?

There are several methods for solving a system of equations, including substitution, elimination, and graphing. Each method involves manipulating the equations to eliminate one variable and solve for the others.

3. Can a system of equations have more than one solution?

Yes, a system of equations can have infinite solutions or no solutions at all. For example, if the equations are equivalent, any value for the variables will make the system true. If the equations are parallel, there is no solution that satisfies both equations.

4. How do I know if my solution to a system of equations is correct?

To check your solution, plug in the values for the variables into each equation and see if they make the equation true. If the values satisfy all of the equations, then your solution is correct.

5. Can I use a calculator to solve a system of equations?

Yes, many calculators have a function for solving systems of equations. However, it is important to understand the concepts and methods behind solving a system of equations in order to use a calculator effectively and check your answers.

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