Set 10: Systems of Equations (Intermediate)

Explanation

Answer: A

Solve: $\begin{cases} x = 3y + 1 \\ 2x + 5y = 13 \end{cases}$

$(7, 2)$

✓ Correct

$(4, 1)$

$(10, 3)$

$(5, \frac{4}{3})$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Since $x = 3 y + 1$ is already isolated, substitute directly. Step 1: Substitute into second equation: $2(3 y + 1) + 5 y = 13$6y + 2 + 5 y = 13$ 11y = 11 $y = 1$$ - First: $$4= 3(1) + 1 = 4$$ ✓ - Second:$ 2(4) + 5(1) = 8 + 5 = 13 $✓ Choice B is incorrect because$ 2(4) + 5(1) = 13 \neq 24 $. Choice C is incorrect because$ 2(10) + 5(3) = 35 \neq 24$. Choice D is incorrect.

Key Steps:

•

The correct answer is $(7, 2)$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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