Starting with system of equations:

x+2y+10a+0b = 30

2x+4y+6a+0b = 20

2x+8y+0a+6b=40

We need to find the values for a and b. Problem is we have three equations and four unknowns. 

Write an augmented matrix using the above equations.

\left|\begin{array}{cccc | c} 1 & 2 & 10 & 0 & 30 // 2 & 4 & 6 & 0 & 20 // 2 & 8 & 0 & 6 & 40 \end{array}\right| 

Begin row-reduction techniques. 

\left|\begin{array}{cccc | c} 0 & 0 & 7 & 0 & 20 // 1 & 2 & 3 & 0 & 10 // 2 & 8 & 0 & 6 & 40 \end{array}\right|