MATH/ALGEBRA PLEASE

Okay, I think I have arrived at all the answer to the questions thrown my way. However, how do I explain what is happening “graphically”, where the services are charging same rate?

: Your company must use a transportation service to shuttle their corporate partners from the airport for a quarterly meeting. Crespo Transportation Service charges $32 initially plus $8 per mile for every mile traveled. Siera Transportation Service charges $24 initially plus $10 per mile for every mile traveled.

Write an equation in two variables (x & y) that illustrates the costs for the Crespo Transportation Service.
y=32+8x

Write an equation in two variables (x & y) that illustrates the costs for the Siera Transportation Service.
y=24+10x

If the trip is 3 miles, how much does each one charge? If the trip is 6 miles, how much does each one charge? Explain
If the trip is 3 miles then Crespo transportation services would charge $56

y=32+8x

y=32+8(3)

y=32+24

y=56

For Siera transportation service if the trip is 3 miles then the total charge would be $54

y=24+10x

y=24+10(3)

y=24+30

y=54

If the trip is 6 miles then Crespo transportation would charge $80.00

y=32+8(6)

y=32+48

y=80

If the trip was 6 miles then siera transportation would charge 84

y=24+10(6)

y=24+60

y=84

l) At what mileage are both services charging the same rate? Explain.
For the last part:

set the two y values equal

24 + 10x = 32 + 8x
2x = 8
x = 4

Explanation:
I will solve for x by subtracting
8x from each side and by
subtracting 24 from each side to arrive at the solution.

8x+32=10x+24

8x-8x+32=10x-8x+24

32=2x+24

32-24=2x+24-24

8=2x

x=4

Check if x = 4

Checking the first equation:
y = 32 + 8(4) = 64

Checking the second equation:
y = 24 + 10(4) = 64

Both solutions check.

Therefore, the mileage that both are charging the same rate is 4 miles.
How do I explain what is happening graphically where the services are charging the same rate? is this answer correct?

Graphically, where the services are charging the same rate, the graphs will intersect. A solution of a system of equations in two variables is an ordered pair that makes both equations true. All points will give a solution, but where the services are charging the same rate, the common points give the common solution. The systems are consistent and the equations are independent.

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