# Question Video: Finding an Augmented Matrix given a System of Equations

Find the augmented matrix for the following system of equations: 𝑥 + 5𝑦 = 3, 3𝑥 + 5𝑦 = 1.

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### Video Transcript

Find the augmented matrix for the following system of equations: 𝑥 plus five 𝑦 equals three, and three 𝑥 plus five 𝑦 equals one.

We begin by rewriting the system of equations by highlighting the 𝑥- and 𝑦-terms. We have two equations in two variables, and these equations have already been ordered so that the 𝑥-terms appear first followed by the 𝑦-terms and then the equal sign of each equation. This means that the augmented matrix has two rows and three columns as shown. We begin by looking at the coefficients of the 𝑥-terms. For the first equation, the coefficient of the 𝑥-term is one. And in the second equation, the coefficient is three. This means that the left column of the matrix is populated with the numbers one and three. The next column is populated by the 𝑦-coefficients, in this case five and five. Finally, the values on the right-hand side of our equations, three and one, complete the matrix. Reading row by row, the completed augmented matrix is one five, three, three, five, one. This corresponds to the system of equations 𝑥 plus five 𝑦 equals three and three 𝑥 plus five 𝑦 equals one.