Question

Write the augmented matrix for the system of equations: -4x + 6y = 1 3x - 7y = 1 a. [-4 6 1; 3 -7 1] b. [-4 3 6; 6 -7 1] c. [-4 6 1; 3 -1 7] d. [4 -6 -1; -3 7 -1]

Answer 1

The correct augmented matrix for the given system of equations is [-4, 6, 1; 3, -7, 1]. Thus the correct option is (d).

Step-by-step explanation:

In the augmented matrix, each row corresponds to an equation in the system, and the entries in each row represent the coefficients of the variables on the left side of the equations followed by the constant term on the right side. For the system of equations
`(-4x + 6y = 1\) and \(3x - 7y = 1\),` the augmented matrix is formed by arranging the coefficients and constants in the given order. Thus the correct option is (d).

The first row represents the coefficients of x and y in the first equation: (-4, 6, followed by the constant term 1. The second row represents the coefficients of x and y in the second equation: 3, -7, followed by the constant term 1. Thus, the correct augmented matrix is [-4, 6, 1; 3, -7, 1].

The other options can be ruled out through a careful comparison of the coefficients and constants. For instance, option b has the coefficients in an incorrect order, option c has an incorrect constant term in the second row, and option d has incorrect signs for the coefficients. Therefore, option a is the accurate representation of the given system of equations in augmented matrix form.