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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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