`y ge -3x +18`
`y ge 9x`
In the xy plane, the point (a,b) lies in the solution set of the system of inequalities above. What is the minimuim poosible value of b ?

Options

A. `1 (1)/(2)`
B. 3
C. `7 (1)/(2)`
D. `13 (1)/(2)`

Answer

D

Explanation

The boundary lines of this saystem of inewualites are `y =-3x + 18 and y =9x.` To find their intersection point, set them equal to each other to get `9x =-3x +18. So, 12x =18and x = 1 (1)/(2).` That represents a, but the questin asks for the value of b. Substitute `1 (1)/(2)` for x in either equation, preferably the simpler one: use `y =9x` to get `y =9 (1)/(2)) =13 (10/(2).` Therefore, (D) is correct.