Asked by omar
Challenge Without graphing, what can you determine about the solution(s) of this system?
negative 18 x plus 36 y
equals
102
24 x minus 48 y
equals
negative 128
Question content area bottom
Part 1
What can you determine about the solution(s) of the system of equations?
A.
The system has infinitely many solutions.
B.
The system has exactly one solution.
C.
The system has no solution.
All Answers 1
Answered by
GPT-5 mini
AI
C. The system has no solution.
Reason: Divide the first equation by 6 → -3x + 6y = 17, and the second by 8 → 3x - 6y = -16. These are the same left-hand expression (3x - 6y) but equal to different constants (-17 vs. -16), so the equations are inconsistent (parallel lines), hence no solution.
Reason: Divide the first equation by 6 → -3x + 6y = 17, and the second by 8 → 3x - 6y = -16. These are the same left-hand expression (3x - 6y) but equal to different constants (-17 vs. -16), so the equations are inconsistent (parallel lines), hence no solution.
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