1. $\begin{aligned} x+y & =4 \\ x-y & =2\end{aligned}$

Step 1 ：Given the system of linear equations: \(x + y = 4\) and \(x - y = 2\)

Step 2 ：We can solve this system by either substitution or elimination method. Here, we will use the elimination method.

Step 3 ：By adding the two equations, we can eliminate y and solve for x.

Step 4 ：Once we have the value of x, we can substitute it into either of the two equations to solve for y.

Step 5 ：The solution to the system of equations is \(x = 3\) and \(y = 1\). This means that these values satisfy both equations.

Step 6 ：Final Answer: The solution to the system of equations is \(\boxed{x = 3}\) and \(\boxed{y = 1}\)