Gabriel is working two summer jobs, making $8 per hour babysitting and making $10 per hour clearing tables. in a given week, he can work at most 18 total hours and must earn a minimum of $160. if xx represents the number of hours babysitting and yy represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

we have been given a piecewise function which has three parts

we can graph each part one by one.

first part is x+1 which is just like equation y=x+1

restriction with first part is x< 0 so that means we can use any number for x which is less than 0 for example x=-1 and x=-2

now plug x=-1 into y=x+1 to get y

y=x+1=-1+1=0

so the point will be (-1,0)

similarly we get another point (-2,-1)

now we graph a line joining both points but keep in mind that line must be on left side of x=0 because of restriction x< 0

same way we can graph 2nd and third parts

if we have < or > then we use open circle.

if we have < = or > = then we use close circle.

so using above information, final graph can be drawn as:

step-by-step explanation:

assume that y=mx+n

you may see as , where

in we change places of numerator and denominator, then we insert an opposite sign

and substitute m=-1/3 in the equation y=mx+n

point (4,2), so we substitute x=4, y=2 to the equation and calculate

the answer is