7
algebra

Verify if (8,5)(8, 5) is the solution to: {2x3y=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

D

No, it only satisfies the first equation

Correct Answer: C

Choice C is the correct answer. Let's substitute (8,5)(8, 5) into both equations.

First equation: 2x3y=12x - 3y = 12(8)3(5)=1615=12(8) - 3(5) = 16 - 15 = 1

Second equation: x+4y=28x + 4y = 288+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.