If a system produces a true statement but the variables drop out, the
system has infinite solutions.
True False

**True.**

If a system of equations simplifies to a true statement (like \(0 = 0\) or \(5 = 5\)) after eliminating the variables, it means that the system has infinitely many solutions. This typically occurs in dependent systems, where the equations represent the same line (or plane in higher dimensions), so all points on the line (or plane) are solutions.

Would you like more details on this concept or how it applies to specific problems?

Here are 5 related questions you might consider:
1. What is the difference between dependent and independent systems of equations?
2. How do you solve a system of linear equations using substitution or elimination?
3. Can a system with more equations than unknowns still have infinite solutions?
4. What does it mean for a system to be inconsistent, and how does that differ from infinite solutions?
5. How can graphing help in visualizing systems with infinite solutions?

**Tip:** When solving a system of equations, always check if the final statement after eliminating variables is either a true or false statement. It can indicate whether the system has infinite solutions or no solution at all.

If a system produces a true statement but the variables drop out, the system has infinite solutions. True or False?

Discover how systems of linear equations can result in infinite solutions when variables drop out, producing a true statement like 0 = 0. Understand dependent systems and how this occurs in Algebra. Suitable for students in Grades 9-12.

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