Choice B is the correct answer. To eliminate $y$, multiply the second equation by 2.

Step 1: Multiply the second equation by 2: $10x - 4y = 22$

Step 2: Add to the first equation: $(3x + 4y) + (10x - 4y) = 27 + 22$$13x = 49$$x = \frac{49}{13}$

Non-integer. - First: $3(5) + 4(3) = 15 + 12 = 27$ ✓

• Second: $5(5) - 2(3) = 25 - 6 = 19 \ eq 11$

Step 1: Multiply second by 2: $10x - 4y = 38$

Step 2: Add: $13x = 65$$x = 5$

Step 3: Substitute: $3(5) + 4y = 27$$15 + 4y = 27$$y = 3$

** 💡 Strategic Tip: Multiplying by 2 turned the $-2y$ into $-4y$ to match the $+4y$ in the first equation.

Choice A is incorrect because$3(4) + 4(\frac{15}{4}) = 12 + 15 = 27$ ✓, but $5(4) - 2(\frac{15}{4}) = 20 - 7.5 = 12.5 \ eq 19$.

Choice C is incorrect because$3(3) + 4(4.5) = 9 + 18 = 27$ ✓, but $5(3) - 2(4.5) = 15 - 9 = 6 \ eq 19$.

Choice D is incorrect because$3(6) + 4(2.25) = 18 + 9 = 27$ ✓, but multiplication in second fails.