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. $\displaystyle \left| \begin{array}{lcr}4e+5f&=&86\\-e+2f&=&11\end{array}\right.$ multiply the 2nd equation by 4: $\displaystyle \left| \begin{array}{lcr}4e+5f&=&86\\-4e+8fe&=&44\end{array}\right.$ and add columnwise:
$\displaystyle 13f=130~\iff~f=10$ . Plug in this result into any of the 2 equations and solve for e. $\displaystyle \left(e=9\right)$
2. Solve the 2nd equation for e: e = 2f - 11 and substitute e by this term in the first equation:
$\displaystyle 4(2f-11)+5f=86~\iff~13f=130$
Plug in the result for f into the 2nd equation.