2

Set 2: Systems of Equations (Advanced)

Explanation

Answer: A

Is the point (2,3)(2, 3) a solution to the system? {x+y=52xy=1\begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases}

A.

Yes

✓ Correct
B.

No

C.

Cannot be determined

D.

Only for the first equation

Detailed Explanation

Choice A is correct. Choice A is the correct answer. To ver Step 1: Check the first equation x+y=5x + y = 5: 2+3=52+ 3 = 5 ✓ (True) Step 2: Check the second equation 2xy=12x - y = 1: 2(2)3=43=12(2) - 3 = 4 - 3 = 1 ✓ (True) Since the point satisfies both equations, (2,3)(2, 3) is indeed a Choice D is incorrect because the point satisfies both equations, not just the first one.

Key Steps:

The correct answer is Yes

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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