Final answer:
The system with no solution is system B, where the two equations given will result in parallel lines and will therefore never intersect to provide a solution.
Step-by-step explanation:
The question asks which system of equations has no solution. To determine this, we need to look for a system where the equations are parallel (have the same slope) but have different y-intercepts, as they will never intersect.
- A. Tz + y = -14, -1427y = 28
- B. Z + y = -1, 2z + 2y = 8
- C. 3z – 3y = 6, -5z - 5y = 15
- D. -1z - 6y = 26, 7z + 3y = -13
We can simplify each system to find slopes and y-intercepts:
- For A, we can't simplify without proper coefficients.
- For B, the second equation simplifies to z + y = 4, which is a multiple of the first equation, indicating they are parallel.
- For C, simplifying gives us z - y = 2 and z + y = -3, which are not multiples, so they are not parallel.
- For D, when simplified, none of them appears to be parallel equations.
So, the system that has no solution is system B, because the simplified forms of the equations indicate they are parallel lines, and therefore will never meet.