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 \(\boxed{y = 1}\)