# Elimination (with fractions)

• Oct 4th 2008, 06:44 PM
largebabies
Elimination (with fractions)
I've thought I had elimination down but adding fractions is making me crazy, help?

The question that I need help on is.

m + 3/4n =4
n - 1/4m = -1
• Oct 4th 2008, 06:46 PM
icemanfan
Is the problem

(1)
$\displaystyle m + \frac{3}{4}n = 4$

$\displaystyle n - \frac{1}{4}m = -1$

or (2)
$\displaystyle m + \frac{3}{4n} = 4$

$\displaystyle n - \frac{1}{4m} = -1$

?
• Oct 4th 2008, 06:49 PM
largebabies
It's the first one.

Forgive me, i'm still new :P
• Oct 4th 2008, 06:55 PM
icemanfan
Well, if you don't like fractions, you can get rid of them.

$\displaystyle m + \frac{3}{4}n = 4$ is equivalent to

$\displaystyle 4m + 3n = 16$

and $\displaystyle n - \frac{1}{4}m = -1$ is equivalent to

$\displaystyle 4n - m = -4$.

If you can handle fractions, the easiest method comes from adding the two equations $\displaystyle m + \frac{3}{4}n = 4$ and $\displaystyle 4n - m = -4$ to obtain $\displaystyle \left(4 + \frac{3}{4}\right)n = 0$, that is, $\displaystyle n = 0$.
From this, $\displaystyle m = 4$ quickly follows.