Carmen is making gift boxes for her friends. It takes her 10 minutes to pack a 4-pound treat box, and it takes her 15 minutes to pack a 2-pound game box. Carmen wants to spend no more than 100 minutes packing boxes, and she can only carry up to 50 pounds in her car.

This graph and system of inequalities represent this situation, where x represents the number of treat boxes and y represents the number of game boxes.
10x + 15y ≤ 100
4x + 2y ≤ 50

solution is valid within the context of the situation is (5,2)

Step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3