Final answer:
To establish the value(s) of b that result in a consistent system, we need to manipulate the given system of equations to find a condition for b that allows the system to have a solution.
Step-by-step explanation:
To determine what value(s) of b make the following system of equations consistent, we need to analyze the system:
- x − y + bz = 1
- − y + 2z = 3
- x − z = 5
A system of equations is consistent if there is at least one set of values for the variables that satisfies all equations in the system. If we can express the system in matrix form, apply Gaussian elimination, or simply manipulate the equations to find a solution, we can determine the condition(s) for b for the system to have a solution. Without further context or additional information from the provided references, it is not possible to determine the value of b. This task would typically involve looking for a relation where the determinant of the coefficient matrix is non-zero (for a unique solution) or using methods such as substitution or elimination to solve the system and find the condition for b.