1. ## Solving Simultaneous Equations

Hi everyone, lately I have attempted to do a simple Simultaneous equations problem and it has stumped me for 2 days. Here is the problem:

$\frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5}$ (i)
$\frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4}$ (ii)

I have attempted to solve this problem in 18 ways and they lead to different answer however non of them are correct (Correct answer: R=3, S=1/2 -Back of the book). Here is one of the attempts:

(i) $20\left ( \frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5}\right )$
$\therefore 12r+8-10s-5=44$
$\therefore 12r-10s=44-8+5$
$\therefore 12r-10s=41$ (iii)

(ii) $12\left ( \frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4} \right )$
$\therefore 9+6r+20-4s=45$
$\therefore 6r-4s=45-9-20$
$\therefore 6r-4s=16$ (iv)

(iv) $2\left ( 6r-4s=16 \right )$
$\therefore 12r-8s=32$ (v)

(iii - v) $-0-2s=9$
$s=4.5$

If someone could explain to me how to do this, I would be really grateful because I'm starting to pull my hair out over this problem I think I'm doing something wrong with the numerators.

2. ## Re: Solving Simultaneous Equations

Originally Posted by tracey3
Hi everyone, lately I have attempted to do a simple Simultaneous equations problem and it has stumped me for 2 days. Here is the problem:

$\frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5}$ (i)
$\frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4}$ (ii)

I have attempted to solve this problem in 18 ways and they lead to different answer however non of them are correct (Correct answer: R=3, S=1/2 -Back of the book). Here is one of the attempts:

(i) $20\left ( \frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5}\right )$
$\therefore 12r+8-10s\color{red}{+}5=44$
$\therefore 12r-10s=44-8\color{red}{-}5$
$\therefore 12r-10s=\color{red}{31}$ (iii)

(ii) $12\left ( \frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4} \right )$
$\therefore 9+6r+20-4s=45$
$\therefore 6r-4s=45-9-20$
$\therefore 6r-4s=16$ (iv)

3. ## Re: Solving Simultaneous Equations

$\frac{3r+2}{5} - \frac{2s-1}{4}=\frac{11}{5}$ (i)
$\frac{3+2r}{4} + \frac{5-s}{3}=\frac{15}{4}$ (ii)

Much easier if you start this way:
(3r + 2) / 5 - 11 / 5 = (2s - 1) / 4 : (3r - 9) / 5 = (2s - 1) / 4

Similarly with equation (ii).

4. ## Re: Solving Simultaneous Equations

Wow, it was such a simple mistake... Every time I try to come up with complex ways of solving this stuff, then its the simple things that catch you out.