Final answer:
The augmented matrix for the system of equations -6x + 4y = -10 and -7x + y = -8 is [-6 4 | -10] and [-7 1 | -8], which includes the coefficients of x, y and the constants from both equations.
Therefore, the augmented matrix is:
[ -6 4 | -10 ]
[ -7 1 | -8 ]
Step-by-step explanation:
To write the augmented matrix for the system of linear equations given by:
- -6x + 4y = -10
- -7x + y = -8
We start by organizing the coefficients of x and y, as well as the constants from the right-hand side of the equations, into rows of a matrix:
The first row comes from the coefficients and constant of the first equation (-6x + 4y = -10), and the second row comes from the second equation (-7x + y = -8).
Therefore, the augmented matrix is:
[ -6 4 | -10 ]
[ -7 1 | -8 ]
This matrix directly represents the system of equations, with the vertical bar indicating the separation between the coefficients and the constants.