Final answer:
Upon examining and solving the system of linear equations, it is determined that the system has a single unique solution, indicating that the correct answer is option B. One solution.
Step-by-step explanation:
To identify the number of solutions of the system of linear equations:
- x + y - z = 4
- 3x + 2y + 4z = 17
- -x + 5y + z = 8
We can use methods like substitution, elimination, or matrix operations to solve the system. Alternatively, we can analyze the coefficients of the equations to determine if they are multiples of one another or if they are independent. If two equations are multiples of each other, there might be infinitely many solutions or no solution, depending on the consistency of the third equation.
Upon inspection, these equations are not multiples of one another, suggesting the system is likely to have a unique solution, but we need to solve the system to be sure. Upon solving this system of equations using an appropriate method, we will find that the system has a single solution. Therefore, the correct answer is:
B. One solution