8.2.41 Solve the following system of equations using matrices (row operations)If

Question

8.2.41 Solve the following system of equations using matrices (row operations)If the system has no solution, say that it is inconsistent. x+5y= 6 2x+ 10y 12 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice O A. The solution is Simplify your answers.) O B. There are infinitely many solutions. The solution can be writen as (yjx yis any real number) (Simplity your answer. Type an expression using y as the variable.) O C. The system is inconsistent Click to select and enter your answer(s) and then click Check Answer All parts showing

Explanation / Answer

x+5y=6

2x+10y=12

=[1 5]

2 10

Clearly =0 and hence it has infinitely many solutions.

From the conditions:

A system has infinitely many solutions when it is consistent and the number of variables is more than the number of nonzero rows in the rref of the matrix.

A system has a unique solution when it is consistent and the number of variables is equal to the number of nonzero rows

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