Given that (3, 2, –6) and (–2, 5, 1) are solutions of two equations in a system of three linear equations, which of the following is true about the system?
a.) the system can only be consistent and independent.
b.) the system can be either inconsistent and independent or consistent and dependent.
c.) the system can be either inconsistent and dependent or consistent and independent.
d.) the system can only be inconsistent and dependent.

The system can be inconsistent or consistent and  independent or consistent and  dependent.

Step-by-step explanation:

Consistent system: When the system of equation have atleast one solution then the system is consistent.

Inconsistent system: When the system of equation have no solution then the system is called inconsistent.

Dependent system: When the consistent system have infinite number of solutions then the system is called dependent.

Independent system: When the consistent system has exact one solution then the system is called independent system.

We are given two solutions of two equations are (3,2,-6) and (-2,5,1).

But the system of equations have three equations.

Then, the system of equations may have no solution or may have altleast one solution.

If given system of equations have no solutions then the system is inconsistent.

If the given system of equations have two or more than two solutions then the system is consistent and dependent.

If the given system of equations has exactly one solution then the system is consistent and independent.

The system can be inconsistent or consistent independent or consistent independent.

1) is right

step-by-step explanation: