Determine the solution of the system of equations:
$\begin{array}{l}2 x-3 y=1 \\ x-y=1\end{array}$

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Answer

Final Answer: The solution to the system of equations is $\boxed{x = 2, y = 1}$

Steps

Step 1 ：We have the system of equations: $\begin{array}{l}2 x-3 y=1 \\ x-y=1\end{array}$

Step 2 ：Let's solve the second equation for x: $x = y + 1$

Step 3 ：Substitute x in the first equation with the expression we got from the second equation: $2*(y + 1) - 3*y = 1$

Step 4 ：Solve for y: $y = 1$

Step 5 ：Substitute y = 1 back into the second equation to solve for x: $x = 1 + 1$

Step 6 ：Solve for x: $x = 2$

Step 7 ：Final Answer: The solution to the system of equations is $\boxed{x = 2, y = 1}$