x-y=3,\\ 2x - 3y = 4

To solve the system of equations \( x - y = 3 \) and \( 2x - 3y = 4 \), we can use the method of substitution or elimination.

Let's use the substitution method. From the first equation, we have \( x = y + 3 \).

Now, substitute this expression for \( x \) in the second equation:

\( 2(y + 3) - 3y = 4 \)

\( 2y + 6 - 3y = 4 \)

\( -y + 6 = 4 \)

\( -y = 4 - 6 \)

\( -y = -2 \)

\( y = 2 \)

Now that we have found the value of \( y \), we can substitute it back into the first equation to find the value of \( x \):

\( x = 2 + 3 \)

\( x = 5 \)

Therefore, the solution to the system of equations is \( x = 5 \) and \( y = 2 \).