Choice C is the correct answer. The $2y$ terms are opposites ($+2y$ and $-2y$), so we can add the equations to eliminate $y$.

Step 1: Add the two equations: $(5x + 2y) + (5x - 2y) = 23 + 17$$10x = 40$$x = 4$

Step 2: Substitute $x = 4$ into the first equation: $5(4) + 2y = 23$$20 + 2y = 23$$2y = 3$$y = \frac{3}{2}$

Solution: $(4, \frac{3}{2})$

Verification: $5(4) - 2(\frac{3}{2}) = 20 - 3 = 17$ ✓

💡 Strategic Tip: Opposite coefficients signal that addition will eliminate the variable cleanly.

Choice A is incorrect because$5(5) + 2(-1) = 25 - 2 = 23$ ✓, but $5(5) - 2(-1) = 25 + 2 = 27 \ eq 17$.

Choice B is incorrect because$5(3) + 2(4) = 15 + 8 = 23$ ✓, but $5(3) - 2(4) = 15 - 8 = 7 \ eq 17$.

Choice D is incorrect because$5(6) - 2(-\frac{7}{2}) = 30 + 7 = 37 \ eq 17$.