Set 7: Systems of Equations (Intermediate)

Choice D is correct. Choice D is the correct answer. The $2y$ terms are opposites, so we add the equations. Step 1: Add the equations: (x + 2 y) + (x - 2 y) = 12 + 4$2x = 16$x = 8 Step 2: Substitute $x = 8$ into the first equation: $$$8+ 2 y = 122y = 4$y = 2 Solution: $(8, 2)$ Verification: $8- 2(2) = 8 - 4 = 4$ ✓ Strategic Tip: When terms are opposites, the system is designed for elimination by addition. Choice A is incorrect because $7+ 2(2.5) = 7 + 5 = 12$ ✓, but $7- 2(2.5) = 7 - 5 = 2 \neq 4$. Choice B is incorrect because $10+ 2(1) = 10 + 2 = 12$ ✓, but $10- 2(1) = 10 - 2 = 8 \neq 4$. Choice C is incorrect because $6+ 2(3) = 6 + 6 = 12$ ✓, but $6- 2(3) = 6 - 6 = 0 \neq 4$.