Set 10: Systems of Equations (Advanced)

Choice D is correct. Choice D is the correct answer. For exactly one solution, the lines must intersect at a single point, which means they must have different slopes. Analysis: - First line has slope = 3 - Second line has slope = $m$ Condition for one solution: $m \neq 3$ Why: - If $m = 3$: both lines have slope 3 but different y-intercepts (5 and -2), making them parallel → no solution - If $m \neq 3$: lines have different slopes → they intersect at exactly one point Strategic Tip: Different slopes guarantee exactly one solution. Choice A is incorrect because while $m = 5$ gives one solution, it's not the only value that works. Choice B is incorrect because while $m = -2$ gives one solution, it's not the only value that works. Choice C is incorrect because $m = 3$ gives no solution (parallel lines), not one solution.