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.