Final answer:
The augmented matrix for the system of equations -6x + 9y = 38 and x - y = 6 is [-6 9 | 38] and [1 -1 | 6]. The matrix is composed of the coefficients of x and y, along with the constants from the equations.
Step-by-step explanation:
To write the augmented matrix for the system of equations provided, we first need to clarify the system of equations as there seems to be a typo in the question. Assuming the system of equations is meant to be:
-6x + 9y = 38
x - y = 6
We then convert this system into an augmented matrix by placing the coefficients of x and y and the constant terms into a matrix format. The augmented matrix looks like this:
[-6 9 | 38]
[ 1 -1 | 6]
The matrix is 'augmented' because it includes the constants from the right-hand side of the equations, separated by a line from the coefficients of the variables.