Set 11: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Substitute the first equation into the second. Step 1: Substitute $y = 5 x - 8$ into $3x + 2 y = 14$: $$$3x + 2(5 x - 8) = 14$3x + 10 x - 16 = 14$13x = 30x = \frac{30}{13}$$ Non-integer. - First: $$2= 5(2) - 8 = 10 - 8 = 2$$ ✓ - Second: 3(2) + 2(2) = 6 + 4 = 10 \neq 14Strategic Tip: When one equation is y = ..., substitution is natural. Choice A is incorrect because $$3\neq 5(3) - 8 = 7$$. Choice B is incorrect because-3 = 5(1) - 8 = -3$✓, but$3(1) + 2(-3) = -3 \neq 10. Choice D is incorrect because $$12= 5(4) - 8 = 12$$ ✓, but 3(4) + 2(12) = 36 \neq 10$.