Solve $$$\begin{cases} a + b = 1 \\ 2 a + b = 7 \end{cases}$$$ for $$$a$$$, $$$b$$$
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Solve $$$\begin{cases} a + b = 1 \\ 2 a + b = 7 \end{cases}$$$ for $$$a$$$, $$$b$$$ using the Gauss-Jordan Elimination method.
Solution
Write down the augmented matrix: $$$\left[\begin{array}{cc|c}1 & 1 & 1\\2 & 1 & 7\end{array}\right]$$$.
Perform the Gauss-Jordan elimination (for steps, see Gauss-Jordan elimination calculator): $$$\left[\begin{array}{cc|c}1 & 1 & 1\\0 & -1 & 5\end{array}\right]$$$.
Back-substitute:
$$$b = \frac{5}{-1} = -5$$$
$$$a = 1 - \left(-5\right) \left(1\right) = 6$$$
Answer
$$$a = 6$$$A
$$$b = -5$$$A