Quadratic Simultaneous Equation

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In summary, to solve the given equations for x, first rearrange the second equation for y and substitute it into the first equation. This will give you an equation entirely in terms of x. Then solve for x using appropriate algebraic techniques.
  • #1
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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  • #2
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.
 
  • #3
[itex]y = 2\sqrt{x}[/itex]
[itex]y = \frac{x^{2}}{4}[/itex]

I still have no idea how to find [itex]x[/itex]
 
  • #4
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.
 

FAQ: Quadratic Simultaneous Equation

What is a quadratic simultaneous equation?

A quadratic simultaneous equation is a system of two equations that contain at least one quadratic term. This means that at least one variable in each equation is squared.

How do you solve a quadratic simultaneous equation?

To solve a quadratic simultaneous equation, you can use substitution or elimination. In substitution, you solve one equation for one variable and then substitute that value into the other equation. In elimination, you manipulate the equations to eliminate one variable and then solve for the remaining variable.

Can a quadratic simultaneous equation have more than two solutions?

Yes, a quadratic simultaneous equation can have more than two solutions. This happens when the two equations intersect at more than two points. These points are known as the solutions or roots of the equations.

What is the difference between a quadratic simultaneous equation and a linear simultaneous equation?

A quadratic simultaneous equation contains at least one quadratic term, while a linear simultaneous equation only contains linear terms (no squared or higher order terms). This means that the solutions to a quadratic simultaneous equation may be more complex and can include imaginary numbers, while the solutions to a linear simultaneous equation will always be real numbers.

Can a quadratic simultaneous equation have no solutions?

Yes, it is possible for a quadratic simultaneous equation to have no solutions. This happens when the two equations do not intersect at any point, meaning there is no solution that satisfies both equations simultaneously. This can also happen when the two equations are parallel and never intersect.

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