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$2 x-2 y=-6$
$-3 x=-6$

$\left(\begin{array}{cc|c}{2} & {-2} & {-6} \\ {-3} & {0} & {-6}\end{array}\right)$

Gauss Jordan Elimination $\longrightarrow$ Reduced Echelon Form

$\left(\begin{array}{cc|c}{2} & {-2} & {-6} \\ {-3} & {0} & {-6}\end{array}\right) R_{1} \rightarrow 1 / 2 R_{1}$

$\left(\begin{array}{cc|c}{1} & {-1} & {-3} \\ {-3} & {0} & {-6}\end{array}\right) R_{2} \rightarrow R_{2}+3 R_{1}$

$\left(\begin{array}{cc|c}{1} & {-1} & {-3} \\ {0} & {-3} & {-15}\end{array}\right) R_{2}\rightarrow -1/3 R_{2}$

$\left(\begin{array}{cc|c}{1} & {-1} & {-3} \\ {0} & {1} & {5}\end{array}\right) R_{1} \rightarrow R_{1}+R_{2}$

$\left(\begin{array}{ll|l}{1} & {0} & {2} \\ {0} & {1} & {5}\end{array}\right)$

$x+0 y=2$
$0 x+1 y=5$

$\left(\begin{array}{l}{x} \\ {y}\end{array}\right)=\left(\begin{array}{l}{2} \\ {5}\end{array}\right) \Rightarrow$ (unique sol)

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