Quadratic Simultaneous Equation

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Homework Help Overview

The problem involves solving a system of quadratic simultaneous equations: y² = 4x and x² = 4y. Participants are exploring methods to find the values of x and y.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to rearrange and substitute values but expresses difficulty in finding a solution. Some participants suggest rearranging one equation to substitute into the other, while others note potential errors in the original poster's approach to solving for y.

Discussion Status

The discussion is ongoing, with participants providing guidance on rearranging equations and questioning the original poster's methods. There is no explicit consensus, as different interpretations of the equations are being explored.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the use of certain resources or methods. There is also a noted confusion regarding the correct application of the equations.

fonz
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Homework Statement


Solve the equation for x

[itex]y^2 = 4x[/itex]

[itex]x^2 = 4y[/itex]

Homework Equations



None

The Attempt at a Solution



[itex]y^2 -4x = x^2 - 4y = 0[/itex]

I have spent ages re-arranging and substituting in values but I just cannot solve this thing.
 
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Why don't you try to rearrange the second equation for y and sub into the first equation. This will give you an equation entirely in terms of x.
 
[itex]y = 2\sqrt{x}[/itex]
[itex]y = \frac{x^{2}}{4}[/itex]

I still have no idea how to find [itex]x[/itex]
 
fonz said:
[itex]y = 2\sqrt{x}[/itex]
[itex]y = \frac{x^{2}}{4}[/itex]

I still have no idea how to find [itex]x[/itex]

You didn't do what CAF123 suggested, which was to solve for y in the second equation, and then substitute for y in the first equation.

You solved for y in the second equation, but then solved for y (incorrectly) in the first equation. Note that if y2 = 4x, then y = 2√x is only one of two solutions.
 

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