Set 12: Systems of Equations (Intermediate)

Choice C is correct. Choice C is the correct answer. We need to multiply both equations to eliminate a variable. Step 1: Multiply first equation by 2 and second by 5: 4x + 10 y = 48$$15x - 10 y = 25 Step 2: Add the equations: $$$19x = 73x = \frac{73}{19}$$ Non-integer. - First: 2(3) + 5(\frac{18}{5}) = 6 + 18 = 24$✓ - Second:$3(3) - 2(\frac{18}{5}) = 9 - \frac{36}{5} = \frac{45-36}{5} = \frac{9}{5} \neq 5$Strategic Tip: When coefficients don't match, multiply both equations to create opposite coefficients. Choice A is incorrect because$2(2) + 5(4) = 24$✓, but$3(2) - 2(4) = -2 \neq \frac{9}{5}$. Choice B is incorrect because$2(4) + 5(3.2) = 24$✓, but substitution in second fails. Choice D is incorrect because$2(5) + 5(2.8) = 24$ ✓, but substitution in second fails.