If a system yields a false statement such as 5 = 4, what does that indicate?

If a system yields a false statement such as 5 = 4, what does that indicate?

• A. One solution
• B. Infinite solutions
• C. No solution
• D. Dependent system

Answer: (C)

When solving a system, you look for a point that satisfies both equations. If you end up with a statement like 5 = 4, that’s a contradiction—something that can’t be true. This shows the two equations cannot be true at the same time for any value of the variables, so there is no point that lies on both lines. In graph terms, the lines are parallel and never intersect, which means there is no solution. If the lines did intersect, there would be exactly one solution. If the two equations were the same line, every point on that line would satisfy both, giving infinitely many solutions.

When solving a system, you look for a point that satisfies both equations. If you end up with a statement like 5 = 4, that’s a contradiction—something that can’t be true. This shows the two equations cannot be true at the same time for any value of the variables, so there is no point that lies on both lines. In graph terms, the lines are parallel and never intersect, which means there is no solution.

If the lines did intersect, there would be exactly one solution. If the two equations were the same line, every point on that line would satisfy both, giving infinitely many solutions.