Solve a written problem with matrix I have the following problem described here:
The government attributes an allocation to the children who benefits child-care services. The children are splitted inside 3 groups: preschool, first cycle and second cycle. The allocation is different for each group, 2$ for the first cycle and the others are unknowns, lets name them x and y. On the other hand, we analysed the following data from 3 different school
Rainbow School: 43 preschool children, 160 first cycle children and 140 second cycle. Total allocation: 589$
Cumulus School: 50, 170, 160 total: k(unknown)
Nimbus School: 100, 88, 80 total: 556$
Now, I must represent the following problem with a matrix equation, I have tried the following:
$$
M = \begin{array}{cccc} 43x & 320 & 140y & 589 \\ 50x & 340 & 160y & k \\ 100x & 176 & 80y & 556 \end{array}
$$
I'm not sure that it make sense and I'm not sure how to solve it either. What now?

There's an easier solution, I think.  Take the Rainbow and Nimbus schools alone. This yields a system of equations:
$$
43x+320+140y=589\\
100x+176+80y=556.
$$
Two variables and two equations means you can find the solutions for $x$ and $y$. Following that, you can plug those values into your formula for Cumulus and find $k$.
EDIT: if you know that $x$ and $y$ are integers, you can plug in some low values and probably find $x,y$ without solving the system properly.
