Set 7: Systems of Equations

Choice C is correct. Choice C is the correct answer. For no solution, we need parallel lines. Step 1: Notice the second equation's coefficients are double the first's: $8x + 10 y = 2(4 x + 5 y)$ Step 2: Multiply the first equation by 2: $$2(4 x + 5 y) = 2(12) = 248x + 10 y = 24$$$ Analysis: - If b = 24$: equations are identical → infinitely many solutions - If$b \neq 24$: parallel lines → no solution Conclusion: Any value except 24 gives no solution. Strategic Tip: When left sides are proportional, the constant determines whether lines are identical or parallel. Choice A is incorrect because$b = 24$gives infinitely many solutions, not no solution. Choice B is incorrect because while$b = 12$gives no solution, it's not the only value. Choice D is incorrect because while$b = 6$ gives no solution, it's not the only value.