The owner of a bike shop sells tricycles (3 wheels) and bicycles (2 wheels), keeping inventory by counting seats and wheels. one day she counts 13 seats and 31 wheels. how many of each type of cycle are there? a. t + b = 13 3t + 2b = 31 b. t + b = 5 3t + 2b = 44 c. t • b = 44 3t + 2b = 13 d. t + b = 31 3t + 2b = 13

A.t + b = 13

3t + 2b = 31

13 is the total made (which counts all tricycles and bicycles)

31 is the total wheels used (so you have to count the amount of wheels used for each bike, and how much of each is made).

hope this helps

(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