Set 11: Systems of Equations (Advanced)

Choice A is correct. Choice A is the correct answer. We'll eliminate $y$ by multiplying the first equation by 2 and the second by 5. Step 1: Multiply the equations: 4x - 10 y = -8$$15x + 10 y = 85 Step 2: Add the equations: 19x = 77$x = \frac{77}{19}$$ Non-integer. - First: $2(3) - 5(2) = 6 - 10 = -4$ ✓ - Second: $3(3) + 2(2) = 9 + 4 = 13 \neq 17$ Step 1: Multiply equations: 4x - 10 y = -815x + 10 y = 65$$$ Step 2: Add: $$$19x = 57$x = 3 Step 3: Substitute: 2(3) - 5 y = -4$6- 5 y = -4$-5 y = -10y = 2 Strategic Tip: When neither coefficient is 1, multiply both equations to create opposite coefficients. Choice B is incorrect because $2(5) - 5(\frac{14}{5}) = 10 - 14 = -4$ ✓, but $3(5) + 2(\frac{14}{5}) = 15 + 5.6 \ e 13$. Choice C is incorrect because $2(4) - 5(\frac{12}{5}) = 8 - 12 = -4$ ✓, but second equation fails. Choice D is incorrect because $2(2) - 5(\frac{8}{5}) = 4 - 8 = -4$ ✓, but second equation fails.