Answer
No. It is not possible to change some constants on the equations’ right sides to make the new system inconsistent.
Work Step by Step
A nonhomogeneous system of linear equations is written in the form Ax = b, where A is a matrix of coefficients, x is a vector of unknowns, and b is a vector of constants. If the system has a solution with two free variables, it means that the rank of the coefficient matrix A is less than the number of unknowns - in our case, 8. Specifically, the rank of A must be 6 or less, since there are 6 equations in the system.
The rank of A is a property of the coefficients alone and is not affected by the constants on the right side of the equations. Therefore, it is not possible to change the constants in b in such a way that the rank of A becomes greater than 6, which would make the system inconsistent.
