### Instruction: If the system of equations

\begin{align*}
2x-y&=a,\\
3y-6x &=b.
\end{align*}has a solution, find $\frac{a}{b},$ assuming $b \neq 0.$.### Response: Let's solve the first equation for y.
y=2x-a.
Now, we can substitute this value for y in the second equation.
So, 3(2x-a)-6x=b.
That simplifies to 6x-3a-6x=b.
Or -3a=b.
So a=-b/3.