Question about this technique for solving simultaneous equations

[chwala]

Homework Statement

See attached

Relevant Equations

understanding of equations

I was going through this...

The steps are quite clear; although i do not know whether it is a general approach to let $y=mx$ in such kind of problems when the degree are the same...second degree, third degree and so on.

My approach to this problem was straightforward;

$y=\dfrac{8-2x^2}{3x}$

thus on substitution to first equation, we shall have,
...
$9x^4+96x^2-24x^4+64-32x^2+4x^4-117x^2=0$

$-11x^4-53x^2+64=0$

Let

$m=x^2$

then it follows that,

$11m^2+53m-64=0$

$m=1, ⇒ x=±1$

The values of $y$ would be found by substituting $x=±1$ into $y=\dfrac{8-2x^2}{3x}$

cheers.

My interest is on the highlighted part.

 

[PeroK]

As is clear from the working, $m$ is a variable, not a constant of proportionality. There was a thread yesterday where a similar approach caused this confusion. In general, as long as $x \ne 0$, you can always set $m = \frac y x$. Personally, I would use $z = \frac y x$, and then it's clearer what's happening.

 

[Mark44]

My interest is on the highlighted part.

I don't see any highlighted part.

 

[haruspex]

I don't see any highlighted part.

I assume it is the passage in lilac: "although i do not know whether it is a general approach to let in such kind of problems when the degree are the same...second degree, third degree and so on."

 

[Mark44]

I assume it is the passage in lilac: "although i do not know whether it is a general approach to let in such kind of problems when the degree are the same...second degree, third degree and so on."

You're right. I thought he meant that something was highlighted in the image from the book. Also, that lilac doesn't really stand out very distinctly.