# Question Video: Finding a System of Equations from a Given Augmented Matrix Mathematics • 10th Grade

Find the system of equations from the following augmented matrix: (7, 2, −7, −5, 4, 6).

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### 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.