Question

1. what result indicates no solution when using elimination?

a. the variables all cancel out to 0
b. the variables are not eliminated
c. the equation simplifies to a false statement like $0=3$
d. the equation reduces to a tautology like $0=0$

Explanation:

When using elimination to solve a system of equations, if all variables cancel out and the remaining equation is a false contradiction (such as $0=3$), this means the system has no solution, as there are no values for the variables that can satisfy the contradictory statement. A tautology like $0=0$ indicates infinitely many solutions, variables not being eliminated means elimination is incomplete, and variables canceling to 0 alone does not define a no-solution case.

Answer:

c. The equation simplifies to a false statement like 0 = 3