8
algebra

Verify if (7,2)(7, 2) is the solution to: {5x3y=292x+4y=22\begin{cases} 5x - 3y = 29 \\ 2x + 4y = 22 \end{cases}

A

No, it only satisfies the first equation

B

No, it satisfies neither equation

C

Yes

D

No, it only satisfies the second equation

Correct Answer: C

Choice C is the correct answer. Let's substitute (7,2)(7, 2) into both equations.

First equation: 5x3y=295x - 3y = 295(7)3(2)=356=295(7) - 3(2) = 35 - 6 = 29

Second equation: 2x+4y=222x + 4y = 222(7)+4(2)=14+8=222(7) + 4(2) = 14 + 8 = 22

Since (7,2)(7, 2) satisfies both equations, it is the Choice A is incorrect because the point satisfies both equations.

Choice B is incorrect because the point does satisfy both equations.

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