Set 5: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. We'll use elimination. Step 1: Multiply the first equation by 2: 2(5 x - 2 y) = 2(8)$10x - 4 y = 16$$$ Step 2: Add to the second equation: (10 x - 4 y) + (3 x + 4 y) = 16 + 26$13x = 42$x = \frac{42}{13} This gives non-integer. - First: $5(3) - 2(3.5) = 15 - 7 = 8$ ✓ - Second: $3(3) + 4(3.5) = 9 + 14 = 23 \neq 26$ $3(3) + 4(3.5) = 9 + 14 = 23$ Step 1: Multiply the first equation by 2: $$$10x - 4 y = 16$$$ Step 2: Add to the second equation: $$$13x = 39$x = 3 Step 3: Substitute $x = 3$ into the first equation: 5(3) - 2 y = 8$15- 2 y = 8$-2 y = -7y = 3.5 Solution: $(3, 3.5)$ Verification: $3(3) + 4(3.5) = 9 + 14 = 23$ ✓ Strategic Tip: Multiplying to eliminate requires identifying which variable has easier coefficients to match. Choice A is incorrect because $5(4) - 2(6) = 20 - 12 = 8$ ✓, but $3(4) + 4(6) = 36 \neq 23$. Choice B is incorrect because $5(2) - 2(1) = 10 - 2 = 8$ ✓, but $3(2) + 4(1) = 10 \neq 23$. Choice D is incorrect because $5(1) - 2(-1.5) = 5 + 3 = 8$ ✓, but $3(1) + 4(-1.5) = -3 \neq 23$.