# Thread: Nonlinear Systems of Equations Problem Exercies

1. ## Nonlinear Systems of Equations Problem Exercies

Nonlinear Systems of Equations Problem ExerciesNonlinear Systems of Equations Problem - YouTube

2. ## Re: Nonlinear Systems of Equations Problem Exercies

To begin with $\displaystyle (2x)^2$ is NOT equal to $\displaystyle 2x^2$.

If $\displaystyle y^2= x^2- 1$ y is NOT equal to $\displaystyle x- 1$

You seem to be having extreme difficulty with square roots! In general [itex]\sqrt{ax^2+ b[/tex] is NOT equal to ax+ b.

3. ## Re: Nonlinear Systems of Equations Problem Exercies

13. $\displaystyle y = \sqrt{x}$ , $\displaystyle y = 2x$

$\displaystyle 2x = \sqrt{x}$

$\displaystyle (2x)^2 = (\sqrt{x})^2$

$\displaystyle 4x^2 = x$

$\displaystyle 4x^2 - x = 0$

$\displaystyle x(4x-1) = 0$

$\displaystyle x = 0 \, , \, x = \frac{1}{4}$

19.

$\displaystyle x^2 + y^2 = 1$

$\displaystyle y = x$

substitute x for y ...

$\displaystyle x^2 + x^2 = 1$

$\displaystyle 2x^2 = 1$

$\displaystyle x^2 = \frac{1}{2}$

$\displaystyle x = \pm \sqrt{\frac{1}{2}}$

btw, regarding your attempt ... note that $\displaystyle \sqrt{-x^2+1} \ne -x + 1$ get that out of your head, NOW.

23.

$\displaystyle 2x^2 - y^2 = 1$

$\displaystyle x^2 - 2y^2 = -1$

multiply the second equation by $\displaystyle -2$ to eliminate the x terms ...

$\displaystyle 2x^2 - y^2 = 1$

$\displaystyle -2x^2 + 4y^2 = 2$

---------------------------

$\displaystyle 3y^2 = 3$

$\displaystyle y = \pm 1$

4. ## Re: Nonlinear Systems of Equations Problem Exercies

It all worked out I got it now. I over emphasized it now. How you guys upload your work on here like that ^? Is that a software or a tool on here? How do I access it?

5. ## Re: Nonlinear Systems of Equations Problem Exercies

it's called Latex ...

LaTeX Help