No solution vs. infinitely many: the SAT math trap

Short answer: Scale one equation to match. Same left side, different right side = parallel lines, no solution.

The trap, in one question

Tempting answer: Infinitely many  (same slope)

Correct answer: No solution  (doubled: 6x − 4y = 10, not 12)

How to spot it in 3 seconds

Scale one equation to match. Same left side, different right side = parallel lines, no solution.

FAQ

What is the no solution vs. infinitely many trap on the SAT?

Example: How many solutions does this system have?3x − 2y = 5 and 6x − 4y = 12 The tempting answer is Infinitely many (same slope); the correct answer is No solution (doubled: 6x − 4y = 10, not 12).

How do you avoid the no solution vs. infinitely many trap?

Scale one equation to match. Same left side, different right side = parallel lines, no solution.

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