Choice D is the correct answer. The $2y$ terms are opposites, so we add the equations.

Step 1: Add the equations: $(x + 2y) + (x - 2y) = 12 + 4$$2x = 16$$x = 8$

Step 2: Substitute $x = 8$ into the first equation: $8 + 2y = 12$$2y = 4$$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 $7 - 2(2.5) = 7 - 5 = 2 \ eq 4$.

Choice B is incorrect because$10 + 2(1) = 10 + 2 = 12$ ✓, but $10 - 2(1) = 10 - 2 = 8 \ eq 4$.

Choice C is incorrect because$6 + 2(3) = 6 + 6 = 12$ ✓, but $6 - 2(3) = 6 - 6 = 0 \ eq 4$.