Choice C is the correct answer. The $3y$ terms are opposites, so we add the equations.

Step 1: Add the equations: $(4x + 3y) + (4x - 3y) = 27 + 13$$8x = 40$$x = 5$

Step 2: Substitute $x = 5$ into the first equation: $4(5) + 3y = 27$$20 + 3y = 27$$3y = 7$$y = \frac{7}{3}$

Solution: $(5, \frac{7}{3})$

Verification: $4(5) - 3(\frac{7}{3}) = 20 - 7 = 13$ ✓

💡 Strategic Tip: Opposite coefficients make addition the ideal elimination strategy.

Choice A is incorrect because$4(6) + 3(1) = 24 + 3 = 27$ ✓, but $4(6) - 3(1) = 24 - 3 = 21 \ eq 13$.

Choice B is incorrect because$4(7) - 3(-\frac{1}{3}) = 28 + 1 = 29 \ eq 13$.

Choice D is incorrect because$4(8) + 3(-\frac{5}{3}) = 32 - 5 = 27$ ✓, but $4(8) - 3(-\frac{5}{3}) = 32 + 5 = 37 \ eq 13$.