Question

Challenge  Without​ graphing, what can you determine about the​ solution(s) of this​ system?
negative 27 x plus 54 y
equals
207
24 x minus 48 y
equals
negative 176
Question content area bottom
Part 1
What can you determine about the​ solution(s) of the system of​ equations?
A.
The system has exactly one solution.
B.
The system has infinitely many solutions.
C.
The system has no solution.

Answer 1

C. The left‑hand coefficients are proportional: multiplying the first equation by -8/9 gives 24x - 48y on the left but 207·(-8/9) = -184 on the right, not -176. So the lines are parallel and the system is inconsistent — no solution.