There are two gas stations near your home. Station A costs $2 to drive there and back, and it sells gas for $2.50/gallon. Station B costs $5 to drive there and back, but it sells gas for $2.25/gallon. a) Let A(x) be the total cost to buy x gallons of gas from station A. Find a linear equation for A(x). b) Let B(x) be the total cost to buy x gallons of gas from station B. Find a linear equation for B(x). c) What amount of gas yields the same total cost from both stations?

a. The linear equation is A(x) = 2.50 x + 2

b. The linear equation is B(x) = 2.25 x + 5

c. The amount of gas yields the same total cost from both stations is 12 gallons

Step-by-step explanation:

The form of the linear function is f(x) = m x + b, where

Let us solve the question

Station A:

∵ Station A costs $2 to drive there and back

- That means the initial amount is 2

∴ b = 2

∵ it sells gas for $2.5/gallon

- That means the price per gallon is $2.50 ⇒ rate of change

∴ m = 2.50

∵ A(x) is the total cost to buy x gallons of gas

- Substitute them in the form of the linear function above

∴ A(x) = 2.50 x + 2

a. The linear equation is A(x) = 2.50 x + 2

Station B:

∵ Station B costs $5 to drive there and back

- That means the initial amount is 5

∴ b = 5

∵ it sells gas for $2.25/gallon

- That means the price per gallon is $2.25 ⇒ rate of change

∴ m = 2.25

∵ B(x) is the total cost to buy x gallons of gas

- Substitute them in the form of the linear function above

∴ B(x) = 2.25 x + 5

b. The linear equation is B(x) = 2.25 x + 5

∵ The costs of the two stations are equal

- Equate A(x) and B(x)

∴ A(x) = B(x)

∴ 2.50 x + 2 = 2.25 x + 5

- Subtract 2.25 x from both sides

∴ 0.25 x + 2 = 5

- Subtract 2 from both sides

∴ 0.25 x = 3

- Divide both sides by 0.25

∴ x = 12

c. The amount of gas yields the same total cost from both stations is 12 gallons

answer:      

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