Determine whether the given point is in the feasible set of this system of inequalities.
\[
\left\{\begin{aligned}
7 x+3 y & \leq 92 \\
x+y & \leq 19 \\
2 x+6 y & \leq 69 ;(8,7) \\
x & \geq 0 \\
y & \geq 0
\end{aligned}\right.
\]
Choose the correct answer below.
No
Yes

Step 1 ：Given the point (8,7) and the system of inequalities: \[\begin{aligned} 7x+3y & \leq 92 \\ x+y & \leq 19 \\ 2x+6y & \leq 69 \\ x & \geq 0 \\ y & \geq 0 \end{aligned}\]

Step 2 ：Substitute x = 8 and y = 7 into each inequality:

Step 3 ：For the first inequality, 7(8) + 3(7) = 56 + 21 = 77 which is less than or equal to 92. So, the first inequality holds true.

Step 4 ：For the second inequality, 8 + 7 = 15 which is less than or equal to 19. So, the second inequality holds true.

Step 5 ：For the third inequality, 2(8) + 6(7) = 16 + 42 = 58 which is less than or equal to 69. So, the third inequality holds true.

Step 6 ：For the fourth inequality, x = 8 which is greater than or equal to 0. So, the fourth inequality holds true.

Step 7 ：For the fifth inequality, y = 7 which is greater than or equal to 0. So, the fifth inequality holds true.

Step 8 ：Since all the inequalities hold true for the point (8,7), the point is in the feasible set of the system of inequalities.

Step 9 ：\(\boxed{\text{Yes}}\)