5a)
$$\begin{array}{l}x+y=3\\ x-y=7\end{array}$$

Step 1 ：$\begin{array}{l}x+y=3\\ x-y=7\end{array}$

Step 2 ：Add the two equations to eliminate one of the variables:

Step 3 ：$x+y+(x-y)=3+7$

Step 4 ：$2x=10$

Step 5 ：Solve for x:

Step 6 ：$x=\frac{10}{2}$

Step 7 ：$\boxed{{\displaystyle x=5}}$

Step 8 ：Substitute the value of x into one of the original equations:

Step 9 ：$5+y=3$

Step 10 ：Solve for y:

Step 11 ：$y=3-5$

Step 12 ：$\boxed{{\displaystyle y=-2}}$

Step 13 ：Final Answer: $\boxed{{\displaystyle x=5,y=-2}}$