1. ## Simultaneous Equations

HI Guys,

Can any body solve these simultaneous equations:

2a + 3(a-b) = 7
4b + 3(b-a) = 1

If anybody could show me how to do these that would be great !!

Thanks!

2. Originally Posted by sparkdog
HI Guys,

Can any body solve these simultaneous equations:

2a + 3(a-b) = 7
4b + 3(b-a) = 1

If anybody could show me how to do these that would be great !!

Thanks!
Well start by simplifying:
$\displaystyle 2a + 3(a - b) = 7 \implies 5a - 3b = 7$
and
$\displaystyle 4b + 3(b - a) = 1 \implies -3a + 7b = 1$

The way I typically solve these is by substitution. For example, solve the bottom equation for a:
$\displaystyle a = \frac{7b - 1}{3}$

Then insert this value for a in to the top equation:
$\displaystyle \frac{5}{3} \cdot (7b - 1) - 3b = 7$

Now solve this for b and then put that into the "a" equation above.

-Dan

3. ## Cheers

Thanks for your help Dan, that great.

Im not sure if you have simplified the 2nd equation correct tho.

The second equation was 4b + 3(b-a) = 1

you had got it as 4b + (3b - a) = 1.

Sorry !

4. Originally Posted by sparkdog
Thanks for your help Dan, that great.

Im not sure if you have simplified the 2nd equation correct tho.

The second equation was 4b + 3(b-a) = 1

you had got it as 4b + (3b - a) = 1.

Sorry !
Whoops! A typo that I carried through. Thanks for the catch.

-Dan