Set 13: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. For infinitely many solutions, the second equation must be a multiple of the first. Step 1: Notice that $9x + 12 y$ is exactly $3(3 x + 4 y)$. Step 2: For the equations to be equivalent: $9x + 12 y = 3(3 x + 4 y) = 3(12) = 36$ Verification: - First equation: $3x + 4 y = 12$ - Second equation (with $b = 36$): $9x + 12 y = 36$ - Divide second by 3: $3x + 4 y = 12$ ✓ (same as first) Strategic Tip: If coefficients are scaled by a factor, the constant must be scaled by the same factor for infinite solutions. Choice A is incorrect because $b = 24$ would give no solution (parallel lines). Choice B is incorrect because $b = 12$ would give no solution. Choice D is incorrect because $b = 48$ would give no solution.