### Video Transcript

Find the system of equations from
the following augmented matrix: seven, two, negative seven, negative five, four,
six.

We begin by assuming that the
variables of this system are 𝑥 and 𝑦, with 𝑥 corresponding to the first column
and 𝑦 corresponding to the second column. If this is the case, this system of
linear equations will take the form shown, where the missing values will be
populated using the augmented matrix. The first column of the augmented
matrix features the coefficients seven and negative five. And these are the coefficients of
the 𝑥-terms in the system of equations. The middle column of the augmented
matrix contains the values two and four, which are the coefficients of the
𝑦-terms. Finally, we use the right most
column of the augmented matrix to populate the remaining blank entries of the
system. These are negative seven and six,
respectively.

The augmented matrix seven, two,
negative seven, negative five, four, six corresponds to the system of equations
seven 𝑥 plus two 𝑦 equals negative seven and negative five 𝑥 plus four 𝑦 equals
six. It is important to note here that
since the example did not specifically state we should have used the variables 𝑥
and 𝑦, we could easily have used other variables, for example, 𝑎 and 𝑏. Our equations would then have been
seven 𝑎 plus two 𝑏 equals negative seven and negative five 𝑎 plus four 𝑏 equals
six.