$\left\{\begin{array}{l}3 x+2 y=5 \\ -3 x+4 y=1\end{array}\right.$

Step 1 ：\(\begin{cases} 3x + 2y = 5 \\ -3x + 4y = 1 \end{cases}\)

Step 2 ：Add the two equations to eliminate the x variable:

Step 3 ：\(3x + 2y + (-3x) + 4y = 5 + 1\)

Step 4 ：\(6y = 6\)

Step 5 ：Divide both sides by 6:

Step 6 ：\(y = \boxed{1}\)

Step 7 ：Substitute the value of y back into one of the original equations to find the value of x:

Step 8 ：\(3x + 2(1) = 5\)

Step 9 ：\(3x + 2 = 5\)

Step 10 ：Subtract 2 from both sides:

Step 11 ：\(3x = 3\)

Step 12 ：Divide both sides by 3:

Step 13 ：\(x = \boxed{1}\)

Step 14 ：Final Answer: \(\boxed{x = 1}\) and \(\boxed{y = 1}\)