# Thread: System of four linear equations

1. ## System of four linear equations

Hi all, having trouble organising this into a system of linear equations: A family has 4 pets. A dog called abel and 3 cats called bella, caleb and diago. Abel weighs as much as the cats all together. Bella is the average weight of the other two cats. caleb weighs twice as much as diago. Without the smallest animal, the other three weigh 28kg together. how can i write this as a system of four linear equations

2. Would the equations be:
a = 3b + 3c + 3d
b = c/2 + d/2
c = 2d
a + b + c = 28

3. Let $\displaystyle x_{1}$=weight of Abel
$\displaystyle x_{2}$=weight of Bella
$\displaystyle x_{3}$=weight of Cabel
$\displaystyle x_{4}$ =weight of Diago

Then equations::

$\displaystyle x_{1} - (x_{2}+x_{3}+x_{4})=0$
$\displaystyle 2x_{2}-(x_{3}+x_{4})=0$
$\displaystyle x_{3}-2x_{4}=0$
$\displaystyle x_{1}+x_{2}+x_{3}=28$

4. I would use the coefficient matrix to solve the system:

$\displaystyle \displaystyle\begin{bmatrix}1&-1&-1&-1&:0\\0&2&-1&-1&:0\\0&0&1&-2&:0\\1&1&1&0&:28\end{bmatrix}$

5. Originally Posted by Oiler
Would the equations be:
a = 3b + 3c + 3d
b = c/2 + d/2
c = 2d
a + b + c = 28
Yout 1st one should be a = b + c + d ; anyhow:

Since c = 2d:
a - b - 3d = 0
a + b + 2d = 28
2b - 3d = 0

Easily solved...