Question

100 POINTS HEELP PLSSS!!!

Answer 1

1. (4, 360)

2. total cost at both repair shops is the same

3. Amy's Auto Repair: $280

Explanation:

Given system of equations:

`\begin{cases}y=100+65x\\y=40+80x\end{cases}`

Question 1

Solve by using the Substitution Method:

`\implies 40+80x=100+65x`

`\implies 40+80x-65x=100+65x-65x`

`\implies 40+15x=100`

`\implies 40+15x-40=100-40`

`\implies 15x=60`

`\implies 15x / 15=60 / 15`

`\implies x=4`

Substitute the found value of x into one of the equations and solve for y:

`\implies y=40+80(4)`

`\implies y=40+320`

`\implies y=360`

Therefore, the point of intersection is (4, 360)

Question 2

The two lines intersect at (4, 360). This means that the total cost at both repair shops is the same when it takes 4 hours to repair the car. The cost at this time is $360.

Question 2

To find the cost at both repair shops if it takes 3 hours to fix the car, substitute x = 3 into both equations and solve for y:

Mike's Repair shop:

`\implies y=100+65(3)`

`\implies y=100+195`

`\implies y=295`

Amy's Auto Repair:

`\implies y=40+80(3)`

`\implies y=40+240`

`\implies y=280`

Therefore, Amy's Auto Repair company is the cheapest at a cost of $280.

Answer 2

See below.

Explanation:

1.

y = 100 + 65x

y = 40 + 80x

100 + 65x = 40 + 80x

-15x = -60

x = 4

y = 100 + 65x = 100 + 260 = 360

(4, 360)

2.

The lines intersect at the point (4, 360).

At the point of intersection, where x = 4, it shows that by doing 4 hours of labor, both shops cost the same.

3.

Mike's:

y = 100 + 65x = 100 + 65(3) = 100 + 195 = 295

Amy's:

y = 40 + 80x = 40 + 80(3) = 40 + 240 = 280

For 3 hours of labor, Amy's shop is cheaper at $280. Mike's costs $295.