The system of equations 2x-3y-5=0, 15y-10x+50=0
- A. has a unique solution
- B. has infinitely many solutions
- C. is inconsistent ✓
- D. is consistent and has exactly two solutions
Correct Answer: C. is inconsistent
Explanation
The equations can be rewritten as 2x - 3y = 5 and -10x + 15y = -50. Dividing the second equation by -5 gives 2x - 3y = 10. The coefficients of x and y match, but the constant terms are different (5 \neq 10). The lines are parallel, so the system has no solution and is inconsistent.
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