# Thread: Simultaneous Literal Equation Help

1. ## Simultaneous Literal Equation Help

Hi, I was wondering if someone could work through this problem for me while showing all the steps. I've been having some trouble with getting them right, i get them ok when they're linear/numerical, however these pro-numerals are putting me off

Code:
x + ay/b = ab
bx - ay = 0
That's the question. So far this is how far I've gotten, however now I'm stumped

Code:
bx = b/ay
Therefore: x = 1/ay

sub the x value into the question's first equation:

1/ay + ay/b = ab

b + (ay)^2 = ab * ayb

b + a^2 * y^2 = a^2 * b^2 * y
Now I'm stumped as how to simplify further.

Also, sorry about not using LaTeX. I was stumped on how to add a line break on the first part. The tutorial says to use \\ to make it go down a line, however it didn't seem to work for me it just removed the space on two lines... what I did was:

Code:
x + \frac{ay}{b} = ab \\
bx - ay = 0
Any help with that as well would be greatly appreciated!
Thanks

EDIT: and if it helps. The answer your supposed to get is: x = ab/2 and y = b^2/2

2. Originally Posted by Rudey
Hi, I was wondering if someone could work through this problem for me while showing all the steps. I've been having some trouble with getting them right, i get them ok when they're linear/numerical, however these pro-numerals are putting me off

Code:
x + ay/b = ab
bx - ay = 0
...
EDIT: and if it helps. The answer your supposed to get is: x = ab/2 and y = b^2/2
$\begin{array}{lcr}x+\dfrac{ay}b &=&ab \\ bx-ay &=&0\end{array}$ $\implies$ $\begin{array}{lcr}bx+ay &=&ab^2 \\ bx-ay &=&0\end{array}$

Now subtract the two lines to get rid of the bx:

$2ay = ab^2~\implies~\boxed{y=\dfrac{b^2}2}$

Add the two lines to get rid of the ay:

$2bx=ab^2~\implies~\boxed{x=\dfrac{ab}2}$

3. Ah, so my substitution was just the hard way to do it.. Hmm, thanks heaps! Could it be done through substitution though?

4. Originally Posted by Rudey
Ah, so my substitution was just the hard way to do it.. Hmm, thanks heaps! Could it be done through substitution though?
Of course.

From the 2nd equation you know that $x = \dfrac{ay}b$

Plug in this term into the first equation:

$\dfrac{ay}b + \dfrac{ay}b = ab~\implies~\dfrac{2a}b y = ab~\implies~y = \dfrac{ab}{\frac{2a}b} = \dfrac{b^2}2$

Solve for x using $y = \dfrac{bx}a$

5. Hi. Thanks heaps for that. I was wondering, is there any site which would have some good problems LITERAL simultaneous equation problems? Just I googled, but I couldn't find much, any suggestions? I'm looking for literal equations, I do the ones with numbers fine, but when it comes to using pronumerals I seem to stuff up. More practice won't hurt :P

Thanks!