Solving set of 2 equations with 3 variables I'm working through an example and my answer is not coming out right. 
Two equations are given and then the solution is shown.
Equations:
$$\begin{aligned}20q_{1}+15q_{2}+7.5q_{3}&=10\\
q_{1}+q_{2}+q_{3}&=1\end{aligned}$$
Solution Given: 
$(X, (1/3)(1-5X), (1/3)(2+2X))$ for arbitrary $X$.
I set up a matrix and solved and my solution is
$((3/2)X+1,(-5/2)X-2,X)$
What's going on here?

Did you set up the matrix equation correctly?
$$\pmatrix{20 & 15 &7.5\\ 1 & 1 & 1}\pmatrix{q_1 \\ q_2\\ q_3} = \pmatrix{10\\1}$$
When I solve it, I get
$q=\pmatrix{-1+\frac{3}{2}X\\2-\frac{5}{2}X\\X}$
Note that you can confirm you did your math wrong somewhere because in your answer $q_1+q_2+q_3 \neq 1$ for every $X$. It does for both mine and the solution (which are in fact the same).
