Solve the system of equations. If the system has no solution, say that it is inc
ID: 3138250 • Letter: S
Question
Solve the system of equations. If the system has no solution, say that it is inconsistent. 5x - 2y z1 x 3y 2z-11 Select the correct choice below and fill in any answer boxes within your choice. O A. The solution of the system is xy and z B. There are infinitely many solutions. Using ordered triplets, the solution can be written as {xy,z)lx-yz any real number OC. There are infinitely many solutions. Using ordered triplets, the solution can be written as (xyz)lxy any real number, z any real number? O D. The system is inconsistent. (Simplify your answers.) (Simplify your answers. Type expressions using z as the variable as needed.) (Simplify your answer. Type an expression using y and z as the variables as needed.)Explanation / Answer
The augmented matrix of the given system of linear equations is A (say) =
1
1
-1
5
5
-2
1
-1
1
3
-2
11
To solve the given system of linear equations, we will reduce A to its RREF as under:
Add -5 times the 1st row to the 2nd row
Add -1 times the 1st row to the 3rd row
Multiply the 2nd row by -1/7
Add -2 times the 2nd row to the 3rd row
Multiply the 3rd row by 7/5
Add 6/7 times the 3rd row to the 2nd row
Add 1 times the 3rd row to the 1st row
Add -1 times the 2nd row to the 1st row
Then the RREF of A is
1
0
0
1
0
1
0
2
0
0
1
-2
It implies that the given system of linear equations has a unique solution x = 1,y = 2 and z = -2.
Option A.
1
1
-1
5
5
-2
1
-1
1
3
-2
11