Question

Identify the augmented matrix for the system of equations and the solution using row operations. 7x − 4y = 28 5x − 2y = 17

Answer 1

The augmented matrix for the system of equations is [7 -4 28] [5 -2 17]. The solution is x = 4 and y = -1.

Step-by-step explanation:

To find the augmented matrix for the system of equations, we can write the coefficients of the variables and their constants in a matrix form. The augmented matrix is a combination of the coefficient matrix and the constant matrix. In this case, the augmented matrix is:

[7 -4 28]

[5 -2 17]

To find the solution using row operations, we need to transform the matrix into reduced row-echelon form. Starting with the first row, we can multiply it by -5/7 and add it to the second row to eliminate the x variable. This gives us a new matrix:

[7 -4 28]

[0 -2 2]

Now, we can multiply the second row by -1/2 to make the coefficient of y 1. The new matrix is:

[7 -4 28]

[0 1 -1]

So the solution to the system of equations is x = 4 and y = -1.