Nonlinear Systems of Equations Problem Exercies

**Melcarthus** · November 11th 2012, 01:31 PM

**HallsofIvy** · November 11th 2012, 02:11 PM

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

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

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

**skeeter** · November 11th 2012, 02:18 PM

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

$2x = \sqrt{x}$

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

$4x^2 = x$

$4x^2 - x = 0$

$x(4x-1) = 0$

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

19.

$x^2 + y^2 = 1$

$y = x$

substitute x for y ...

$x^2 + x^2 = 1$

$2x^2 = 1$

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

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

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

23.

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

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

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

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

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

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

$3y^2 = 3$

$y = \pm 1$

**Melcarthus** · November 11th 2012, 04:18 PM

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?

**skeeter** · November 11th 2012, 05:03 PM

it's called Latex ...

LaTeX Help

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