Set 15: Systems of Equations (Intermediate)

Explanation

Answer: C

Verify if $(8, 5)$ is the solution to: $\begin{cases} 2x - 3y = 1 \\ x + 4y = 28 \end{cases}$

No, it only satisfies the second equation

No, it satisfies neither equation

Yes

✓ Correct

No, it only satisfies the first equation

Detailed Explanation

Choice C is correct. Choice C is the correct answer. First equation: $2x - 3 y = 12(8) - 3(5) = 16 - 15 = 1$ ✓ Second equation: $x + 4 y = 28$ $8+ 4(5) = 8 + 20 = 28$ ✓ Since $(8, 5)$ satisfies both equations, it is the Choice A is incorrect because it satisfies both. Choice B is incorrect because it satisfies both. Choice D is incorrect because it satisfies both.

Key Steps:

•

The correct answer is Yes

Why others are wrong:

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

B: Choice B 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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