what would the following system of equations look like in augmented matrix form?
x + y = 5
3x - y = -1
In linear algebra, an augmented matrix is used to represent a system of linear equations. It consists of the coefficients of the variables along with the constants from the right side of the equations aligned in a single matrix.
Given the system of equations:
1. \$x + y = 5\$
2. \$3x - y = -1\$
The coefficients of \$x\$ and \$y\$ from the first equation are 1 and 1, and from the second equation, they are 3 and -1. The constants are 5 and -1. The augmented matrix form for this system would be:
\[
\begin{bmatrix}
1 & 1 & | & 5 \\
3 & -1 & | & -1 \\
\end{bmatrix}
\]
The lines in the augmented matrix separate the coefficients on the left from the constants on the right, similar to how the equal sign separates them in the equations themselves.