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.

Related calculator: System of Equations Calculator

Comma-separated, for example, x+2y=5,3x+5y=14.
Leave empty for autodetection or specify variables like x,y (comma-separated).

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your Input

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