Solve $$$\begin{cases} a + b = 1 \\ - a + 3 b = 2 \end{cases}$$$ for $$$a$$$, $$$b$$$

Solve $$$\begin{cases} a + b = 1 \\ - a + 3 b = 2 \end{cases}$$$ for $$$a$$$, $$$b$$$ using the Gauss-Jordan Elimination method.

Write down the augmented matrix: $$$\left[\begin{array}{ccc}1 & 1 & 1\\-1 & 3 & 2\end{array}\right]$$$.

Perform the Gauss-Jordan elimination (for steps, see Gauss-Jordan elimination calculator): $$$\left[\begin{array}{ccc}1 & 1 & 1\\0 & 4 & 3\end{array}\right]$$$.

Back-substitute:

$$$b = \frac{3}{4}$$$

$$$a = 1 - \left(\frac{3}{4}\right) \left(1\right) = \frac{1}{4}$$$

$$$a = \frac{1}{4} = 0.25$$$A

$$$b = \frac{3}{4} = 0.75$$$A