Is there a general rule for when to solve for "X" or "Y"

[tomslawsky]

In two variable-two equation systems, the Official guide, I noticed when the variables are of the form "X" and "Y", tend to olve for Y in terms of X. I was wondering if it is usually wise to try to solve for the "Y" or "B" (rather than "A") on the GMAT. It seems as if we guess wrong, the calculations can get real cumbersome, real quick.

[ronaldramlan]

I find it logical to substitute a variable with the other variable that you are asked with. So in your case with X and Y, it really depends on which variable does the question ask you to solve. If the question asks you for the number of Y, you'll be better off substituting X with Y.

[mschwrtz]

All other things being equal, if you eventually want to solve for x, and you're solving by substitution, then you may as well solve first for y in terms of x, in order to eliminate y.

But all other things aren't usually equal. Suppose we are asked to solve for x in the following system of equations:

3y-x=7
3x-2y=14

(You might solve by simultaneous solution, but let's ignore that for this question).


If you solve for y in terms of x, you're asking for trouble,

y=(x+7)/3

3x-2((x+7)/3)=14

Oooh, my head hurts.

If you solve for x in terms of y, not so bad,

x=3y-7
3(3y-7)-2y=14
7y-21=14
7y=35
y=5

Plug 5 in for y in either of the original equations to get x=8.

It's not too hard to tell which way is likely to cause trouble. Multiplying is easier than dividing, adding is a little easier than subtracting, squaring is easier than taking the square root, etc.

In Word Translation problems in which you use some sort of a chart, you often solve for the value that ends up in one cell of the chart. There, too, take the path of least resistance; if they want Tom's age in 5 years, but it's easiest to solve for everything in terms of Prachi's current age, then treat Prachi's current age as the variable.