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

Step 1 ：$\{\begin{array}{l}3x+2y=5\\ -3x+4y=1\end{array}$

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 ：$y=\boxed{{\displaystyle 1}}$

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 ：$x=\boxed{{\displaystyle 1}}$

Step 14 ：Final Answer: $\boxed{{\displaystyle x=1}}$ and $\boxed{{\displaystyle y=1}}$