Answer
See below:
Work Step by Step
In each equation in the system, find the intercepts.
Consider the first equation \[y=-x+5\]
\[y\text{-intercept}\]: Set x = 0
\[y=5\]
\[x\text{-intercept}\]: Set y = 0
\[x=5\]
So, the line passes through \[\left( 0,5 \right)\] and \[\left( 5,0 \right)\]
Now, consider the second equation \[2x-y=4\]
\[y\text{-intercept}\]: Set x = 0
\[y=-4\]
\[x\text{-intercept}\]: Set y = 0
\[x=2\]
So, the line passes through \[\left( 0,-4 \right)\] and \[\left( 2,0 \right)\]
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 \[\left( 3,2 \right)\].
Now, check this point in both the equations,
Put \[\left( 3,2 \right)\]in \[y=-x+5\],
\[\begin{align}
& 2=-3+5 \\
& 2=2
\end{align}\]
Which is true.
Now, Put \[\left( 3,2 \right)\]in \[2x-y=4\],
\[\begin{align}
& 2\left( 3 \right)-2=4 \\
& 4=4
\end{align}\]
Which is true.
Hence, both the equations are verified.
Hence, solution of the system is,\[\left\{ \left( 3,2 \right) \right\}\].
