Set 8: Systems of Equations

Choice A is correct. Choice A is the correct answer. Step 1: Isolate $x$ in the second equation: $x = 8 - 2 y$ Step 2: Substitute into the first equation: 3(8 - 2 y) - 4 y = 10$24- 6 y - 4 y = 1024- 10 y = 10-10 y = -14y = 1.4$$ - First: 3(6) - 4(1) = 18 - 4 = 14 \neq 10- Second: $$6+ 2(1) = 8$$ ✓ Step 1: Isolatex in the second equation: $$x = 8 - 2 y$$ Step 2: Substitute into the first equation: $$3(8 - 2 y) - 4 y = 1424- 6 y - 4 y = 14-10 y = -10y = 1$$ Step 3: Find x: $$x = 8 - 2(1) = 6$$ Solution: (6, 1)$Verification:$3(6) - 4(1) = 14✓ and $$6+ 2(1) = 8$$ ✓ Strategic Tip: Isolate the variable with coefficient 1 for simpler substitution. Choice B is incorrect because3(4) - 4(\frac{1}{2}) = 12 - 2 = 10...wait that works! But $$4+ 2(\frac{1}{2}) = 5 \neq 8$$. Choice C is incorrect because $$2+ 2(3) = 8$$ ✓, but 3(2) - 4(3) = -6 \neq 14$. Choice D is incorrect because$3(8) - 4(0) = 24 \neq 14$.