Final answer:
To write an augmented matrix representing the system of equations 5x - 3y = -25 and 4x - y = -13, transform the matrix into row echelon form, and state the solution as an ordered pair. The solution to the system of equations is (-4, -1).
Step-by-step explanation:
To write an augmented matrix representing the system of equations 5x - 3y = -25 and 4x - y = -13, we can arrange the coefficients of the variables in a matrix form with the constants on the right side. The augmented matrix would be:
[5 -3 | -25]
[4 -1 | -13]
To solve the system by transforming the matrix into row echelon form, we can use row operations to eliminate variables. After performing the necessary operations, we obtain the row echelon form as:
[1 0 | -4]
[0 1 | -1]
From this form, we can see that x = -4 and y = -1. Therefore, the solution to the system of equations is (-4, -1).