How can I Solve for a and b in a Simultaneous Equation Quickly?

[boneill3]

Homework Statement

Solve for a and b

$\frac{a}{3}+\frac{b}{4}=1$

Homework Equations

The Attempt at a Solution

My Teacher went straight from:

$\frac{a}{3}+\frac{b}{4}=1$

To

$a = 2\left(1-\frac{b}{3}\right)$

I was wondering If there is a nice trick to get to that step so quickly.

When I try the first thing I do is:

$\frac{a}{3} = 1 - \left(\frac{b}{4}\right)$

than:

$a = \left[1 - \left(\frac{b}{4}\right)\right]\times 3$

and I end up with

$a=\frac{-3(b-4)}{4}$

So mine seems a lot more messy and I'm not sure how he gets to:

$a = 2\left(1-\frac{b}{3}\right)$

Regards

 

[statdad]

Your answer seems to be the correct one - I'm not sure what your teacher was thinking (unless there is a part of the problem you didn't provide).
One more question: since you ask about solving for $$a$$ and $$b$$, is there another equation? A single equation is not
a set of simultaneous equations.

 

[Mark44]

Since you and your teacher both solve the same equation for a and got different solutions, and the two are obviously different, you can easily determine that one of them (at least) is incorrect. Just replace a in the original equation by your expression for a. If you get an identically true statement, then your solution is correct. Similarly, if you replace a by the expression your teacher shows, then his/her solution is correct.