Use the Gauss-Jordan Method to Solve the System of Equations $\begin{array}{l}x+y=1 \\x-y=-4\end{array}$

Multiple Choice

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the
solution with y arbitrary.
- $\begin{array}{l}x+y=1 \\x-y=-4\end{array}$

A) $\left\{ \left( \frac { 5 } { 2 } , - 2 \right) \right\}$
B) $\left\{ \left( - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right) \right\}$
C) $\left\{ \left( - \frac { 3 } { 2 } , \frac { 5 } { 2 } \right) \right\}$
D) $\varnothing$