Jordan is deciding between two parking garages. Garage A charges an initial fee of $9 to park plus $4 per hour. Garage B charges an initial fee of $3 to park plus $6 per hour. Let AA represent the amount Garage A would charge if Jordan parks for tt hours, and let BB represent the amount Garage B would charge if Jordan parks for tt hours. Write an equation for each situation, in terms of t, t, and determine the hours parked, t, t, that would make the cost of each garage the same.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is