SAT-Style: Systems with No Solution / Infinite Solutions

SAT Math · Axiom Academy

Systems: No Solution vs Infinite Solutions When systems don't have exactly one solution Lines intersect at exactly one point. Lines are parallel (never intersect). During solving: Get a contradiction like 0 = 5 Both equations represent the same line. During solving: Get a true statement like 0 = 0 Example 1: No Solution (Parallel Lines) Example 2: Infinite Solutions (Same Line) Spotting No Solution (Before Solving) Spotting Infinite Solutions (Before Solving) Set up the system from the problem. Try to solve using substitution or elimination. Check what you get: An (x, y) pair? → ONE SOLUTION (answer is the point) A false statement like 0 = 5 ? → NO SOLUTION (answer: "no solution") A true statement like 0 = 0 ? → INFINITE SOLUTIONS (answer: "all points on the line") When you see 0 = 0: The system is DEPENDENT (infinite solutions). All points on the line work. When you see 0 = (non-zero): The system is INCONSISTENT (no solution). The equations contradict. Spot parallel lines early: Compare coefficients. If slope is the same but y-intercepts differ, you have parallel lines. No solution and infinite solutions are rarer on SAT, but they do appear. Know the signs!

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