# [SOLVED] Simultaneous equation

• Jan 2nd 2008, 01:27 AM
vincenzo
[SOLVED] Simultaneous equation
Solve the pair of simultaneous equations.

4e + 5f = 86
2f - e = 11
• Jan 2nd 2008, 01:46 AM
earboth
Quote:

Originally Posted by vincenzo
Solve the pair of simultaneous equations.

4e + 5f = 86
2f - e = 11

Hello,

there are a lot of different methods to solve this system of simultaneous equations. I'll demonstrate 2 of them:

First rearrange the 2nd equation!

1. $\left| \begin{array}{lcr}4e+5f&=&86\\-e+2f&=&11\end{array}\right.$ multiply the 2nd equation by 4: $\left| \begin{array}{lcr}4e+5f&=&86\\-4e+8fe&=&44\end{array}\right.$ and add columnwise:

$13f=130~\iff~f=10$ . Plug in this result into any of the 2 equations and solve for e. $\left(e=9\right)$

2. Solve the 2nd equation for e: e = 2f - 11 and substitute e by this term in the first equation:

$4(2f-11)+5f=86~\iff~13f=130$

Plug in the result for f into the 2nd equation.