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.