Find all the solutions to the linear system:
System of uqations:
\[x + y = 5\]
\[2x − y = 3\]
Solve both equations for y
\[y = 5 - x\]
\[y = 2x - 3\]
Make them equal and solve for x
\[2x - 3 = 5 - x\]
\[3x = 8\]
\[x = \frac{8}{3}\]
Plug x into any one of the orginial equations and solve for y
\[\frac{8}{3} + y = 5\]
\[y = 5 - \frac{8}{3}\]
\[y = \frac{7}{3}\]
The solution set for this system of equations is \[x = \frac{8}{3}\] and \[y = \frac{7}{3}\]