Set 8: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Step 1: Multiply the second equation by 2: $6x + 2 y = 26$ Step 2: Add to the first equation: (6 x - 2 y) + (6 x + 2 y) = 14 + 26$12x = 40$x = \frac{10}{3} Non-integer. - First: $6(3) - 2(4) = 18 - 8 = 10 \neq 14$ - Second: $3(3) + 4 = 13$ ✓ $6(3) - 2(4) = 10$, so $6x - 2 y = 10$. Step 1: Multiply second by 2: $6x + 2 y = 26$ Step 2: Add to first: $$$12x = 36x = 3$$ Step 3: Substitute: $$3(3) + y = 13y = 4$$ Solution: (3, 4)$Verification:$6(3) - 2(4) = 10$✓ and$3(3) + 4 = 13$✓ Strategic Tip: Multiplying to match coefficients is often faster than isolating variables. Choice A is incorrect—this was the intermediate calculation error. Choice B is incorrect because$6(2) - 2(-1) = 14$✓, but$3(2) + (-1) = 5 \neq 13$. Choice D is incorrect because$6(4) - 2(1) = 22 \neq 10$.