Set 4: Systems of Equations

Choice C is correct. Choice C is the correct answer. For infinitely many solutions, the equations must be multiples of each other. Step 1: Notice the first equation's coefficients are 4 times the second's: $8x - 12 y = 4(2 x - 3 y)$ Step 2: Divide the first equation by 4: \frac{8 x - 12 y}{4} = \frac{20}{4}$2x - 3 y = 5$$$ Verification: With $k = 5$, multiply second by 4: 4(2 x - 3 y) = 4(5) = 208x - 12 y = 20$$$ ✓ (matches first equation) Strategic Tip: If coefficients are scaled by factor n$, the constant must also be scaled by$n$. Choice A is incorrect because$k = 20$would give parallel lines (no solution). Choice B is incorrect because$k = 8$would give parallel lines. Choice D is incorrect because$k = 10$ would give parallel lines.