The correct answer is: A. 7a – b – c = 0
A system of linear equations is consistent if it has at least one solution. A system of linear equations is said to be dependent if it has infinitely many solutions, and independent if it has exactly one solution.
To determine whether a system of linear equations is consistent, we can use the following theorem:
A system of linear equations is consistent if and only if the determinant of the coefficient matrix is not equal to zero.
In this case, the coefficient matrix is:
[1 2 -3]
[2 3 3]
[5 9 -6]
The determinant of this matrix is:
7a – b – c
Therefore, the system of linear equations is consistent if and only if 7a – b – c is not equal to zero.
Option A: 7a – b – c = 0
This option satisfies the condition that 7a – b – c is not
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