7
algebra

Verify if (2,5)(2, 5) is the solution to: {3x+2y=16xy=3\begin{cases} 3x + 2y = 16 \\ x - y = -3 \end{cases}

A

No, it satisfies neither equation

B

Yes

C

No, it only satisfies the first equation

D

No, it only satisfies the second equation

Correct Answer: B

Choice B is the correct answer. Let's substitute (2,5)(2, 5) into both equations.

First equation: 3x+2y=163x + 2y = 163(2)+2(5)=6+10=163(2) + 2(5) = 6 + 10 = 16

Second equation: xy=3x - y = -325=32 - 5 = -3

Since (2,5)(2, 5) satisfies both equations, it is the Choice A is incorrect because the point satisfies both equations.

Choice C is incorrect because the point satisfies both, not just the first.

Choice D is incorrect because the point satisfies both, not just the second.