Adelivery truck is transporting boxes of two sizes: large and small. the combined weight of a large box and a small box is 60 pounds. the truck is transporting 65 large boxes and 70 small boxes. if the truck is carrying a total of 4000 pounds in boxes, how much does each type of box weigh?

Let a = weight of large box in pounds

Let b = weight of small box in pounds

(1) 65a + 70b=4000

(2) a+b=60

Now we can simultaneously solve these equations.

a = 60 - b. Hence 65(60 - b) + 70b = 4000 So 3900 + 5b = 4000 and 100 = 5b hence b = 20.

SImilarly a = 40. Now we can verify too by putting in the calculated values.

(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