Answer
See below:
Work Step by Step
In each equation in the system, find the intercepts.
Consider the first equation,
\[x+y=5\]
y-intercept: Set x = 0
\[y=5\]
x-intercept: Set y = 0
\[x=5\]
So, the line passes through \[\left( 0,5 \right)\] and \[\left( 5,0 \right)\].
Now, consider the second equation:
\[3x-y=3\]
y-intercept: Set x = 0
\[y=3\]
x-intercept: Set y = 0
\[\begin{align}
& 3x=3 \\
& x=1
\end{align}\]
So, the line passes through \[\left( 0,3 \right)\] and \[\left( 1,0 \right)\].
So, the intersection of both equations can be obtained by graphing them in the same plane as shown below:
So, coordinates of the intersection point is \[\left( 2,3 \right)\].
Now, check this point in both the equations:
Put \[\left( 2,3 \right)\] in \[x+y=5\],
\[\begin{align}
& 2+3=5 \\
& 5=5
\end{align}\]
which is true.
Now, put \[\left( 2,3 \right)\] in \[3x-y=3\],
\[\begin{align}
& 3\left( 2 \right)-3=3 \\
& 3=3
\end{align}\]
which is true.
Hence, both the equations are verified.
