Question

Identify the augmented matrix for the system of equations and the solution using row operations:

7x 4y = 28
5x - 2y = 17
a. [7 5 │28] (3,- 2.5)
[-4 -2│17]

b. [7 -4│ 28] (3,- 2.5)
[5 -2│17]

c. [7 5│ 28] (2,- 3.5)
[-4 -2│17]

d. [7 5│ 28] (2,-3.5)
[5 -2│17]

Answer 1

The augmented matrix for the system of equations is [7 4 │ 28] 5 -2 │ 17. The solution to the system of equations is x = 21/34 and y = 623/34.

Step-by-step explanation:

The augmented matrix for the given system of equations is:

[7 4 | 28]

5 -2 | 17

Using row operations, we can solve the system of equations as follows:

1. First, multiply the first row by 5 and the second row by 7 to eliminate the x-term in the second equation:
2. [35 20 | 140]
3. 35 -14 | 119
4. Next, subtract the second row from the first row:
5. [0 34 | 21]
6. 35 -14 | 119
7. Divide the first row by 34 to get:
8. [0 1 | 21/34]
9. 35 -14 | 119
10. Finally, add 14 times the first row to the second row:
11. [0 1 | 21/34]
12. 0 0 | 623/34

The solution to the system of equations is x = 21/34 and y = 623/34.