# Thread: Simultaneous equations in matrices

1. ## Simultaneous equations in matrices

Hi

I'm having a little problem solving simultaneous equations in matrices.

2b + t = 14
5b + 5t = 40

[2 1] [b] [14]
[5 5] [t] [40]

1
_____

=

1
_____
(2x5) - (1x5) = 5

[5 -1] [14]
[-5 2] [40]

Then how do I go from there to get:

x(b) = 6
y(t) = 2

I just don't know how to do it

2. What is that you're doing? Are you supposed to solve by using some particular method? Are you maybe using Cramer's Rule...?

Thank you!

3. $\displaystyle \begin{pmatrix} 2&1\\ 5&5 \end{pmatrix} \begin{pmatrix} b\\ t \end{pmatrix}=\begin{pmatrix} 14\\ 40 \end{pmatrix}$

$\displaystyle \begin{pmatrix} b\\ t \end{pmatrix}=\frac{1}{5} \begin{pmatrix} 5&{-1}\\ {-5}&{2} \end{pmatrix}\begin{pmatrix} 14\\ 40 \end{pmatrix}$

can you solve it from there?