# Thread: Finding substitution for simultaneous equation

1. ## Finding substitution for simultaneous equation

Hi,

I'm a bit stuck with trying to solve these simultaneous equations:

k(k-m) =12
k(k+m) = 60

I'm familiar with the substitution process when one is clearly linear and the other a polynomial but both are polynomials here and I've tried to find m in terms of k but keep getting wrong answers. Help appreciated.

2. ## Re: Finding substitution for simultaneous equation

$\displaystyle k-m = \frac{12}{k}$

$\displaystyle k+m=\frac{60}{k}$

$\displaystyle (k-m) + (k+m) = 2k = \frac{72}{k}$

$\displaystyle k^2=36$

Double post.

4. ## Re: Finding substitution for simultaneous equation

Not sure I follow that - I thought one would have to find m in terms of K so be able to isolate m ?

5. ## Re: Finding substitution for simultaneous equation

That makes sense to me now! Thanks!

6. ## Re: Finding substitution for simultaneous equation

Originally Posted by Simonsky
I'm a bit stuck with trying to solve these simultaneous equations:
\begin{align*}k(k-m) &=12 \\k(k+m) &= 60 \end{align*}
We can just add to get
$2k^2=72$ or $k^2=36$ giving $k=\pm 6$.

7. ## Re: Finding substitution for simultaneous equation

Thanks -I got obsessed with isolating 'm' when it was quite easy to solve!

8. ## Re: Finding substitution for simultaneous equation

It's usually better to think in terms of eliminating a variable rather than isolating it.