6

Set 7: Systems of Equations

Explanation

Answer: C

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

A.

No, it only satisfies the second equation

B.

No, it satisfies neither equation

C.

Yes

✓ Correct
D.

No, it only satisfies the first equation

Detailed Explanation

Choice C is correct. Choice C is the correct answer. First equation: 2x−3y=12(8)−3(5)=16−15=12x - 3 y = 12(8) - 3(5) = 16 - 15 = 1 ✓ Second equation: x+4y=28x + 4 y = 28 8+4(5)=8+20=288+ 4(5) = 8 + 20 = 28 ✓ Since (8,5)(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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