Question

Solve using augmented matrices.

x+y=1

3x−y=7

Answer 1

To solve the system of equations using augmented matrices, we need to represent the system in matrix form and perform row operations to convert the system into row-echelon or reduced row-echelon form. Then, we can read off the solutions of the system from the matrix.

Step-by-step explanation:

To solve the system of equations using augmented matrices, we need to represent the system in matrix form and perform row operations to convert the system into row-echelon form or reduced row-echelon form.

1. First, write down the coefficients of the variables and the constants in the system of equations as a matrix. This is called the augmented matrix.
2. Perform row operations to transform the augmented matrix into row-echelon form or reduced row-echelon form.
3. Once the augmented matrix is in row-echelon form or reduced row-echelon form, read off the solutions of the system from the matrix.

For the given system of equations x + y = 1 and 3x - y = 7, the augmented matrix is:

[1 1 | 1]

[3 -1 | 7]

Performing row operations, we can convert the augmented matrix into row-echelon or reduced row-echelon form to solve the system.