Simultaneous equations in matrices

Spykerwolf · #1 $Old$ May 4th, 2009, 04:56 AM

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
_____
ad-bc

=

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

stapel · #2 $Old$ May 4th, 2009, 06:26 AM

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!

Showcase_22 · #3 $Old$ May 4th, 2009, 07:45 AM

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

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

can you solve it from there?