Solve the system by elimination.
\[
\left\{\begin{array}{l}
x+y=4 \\
-x-3 y=-6
\end{array}\right.
\]
No solution
Infinite number of solutions

Step 1 ：The system of equations is given as: \[\left\{\begin{array}{l} x+y=4 \\ -x-3 y=-6 \end{array}\right.\]

Step 2 ：We can solve this system by elimination. This involves adding or subtracting the equations in order to eliminate one of the variables, making it possible to solve for the other variable.

Step 3 ：In this case, we can add the two equations together to eliminate x.

Step 4 ：The solution to the system of equations is x = 3 and y = 1. This means that these values of x and y satisfy both equations simultaneously.

Step 5 ：Final Answer: The solution to the system of equations is \(\boxed{x = 3}\) and \(\boxed{y = 1}\).