Answer:
none of these has "no solution"
Step-by-step explanation:
A. The solution is (8/3, 3)
B. The second equation is -1/2 times the first, so these describe the same line. The system has an infinite number of solutions.
C. The solution is (-4, -2)
D. The solution is (4, -2)
E. The second equation is 2 times the first, so these describe the same line. The system has an infinite number of solutions.
_____
A system of equations will have "no solution" when it describes parallel lines—lines that do not intersect. In standard form, such equations are recognizable by their different constants. For example,
- 3x -4y = -4
- 3x -4y = 20 . . . . . . 20 is different from -4
have different constants, so the equations describe parallel lines.
We could multiply one of these by -2 and the system would still be "inconsistent"—having no solution.