# Solve $\begin{cases} a + b = 1 \\ 2 a + b = 7 \end{cases}$ for $a$, $b$

The calculator will solve the system of linear equations $\begin{cases} a + b = 1 \\ 2 a + b = 7 \end{cases}$ for $a$, $b$, with steps shown.

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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:

$b = \frac{5}{-1} = -5$

$a = 1 - \left(-5\right) \left(1\right) = 6$

$a = 6$A
$b = -5$A