Question

The mechanics at Giuseppe’s Auto House specialize in changing fuel injection units and transmissions. Last week, they changed 5 fuel injection units and 10 transmissions and billed 70 hours. This week, they changed 8 fuel injection units and 8 transmissions and billed 64 hours. Let x represent the number of hours to change a fuel injection unit and y represent the number of hours to change a transmission.

5 x + 10 y = 70. 8 x + 8 y = 64.

What is the solution to the system that represents this scenario?
(5, 8)
(2, 6)
(4, 14)
(7, 8)

Answer 1

To solve the system of equations, we can use the elimination method. By multiplying the equations and subtracting them, we find that x = 2 and y = 6. Therefore, the solution is (2, 6).

Step-by-step explanation:

To solve the system of equations 5x + 10y = 70 and 8x + 8y = 64, we can use either substitution or elimination method. Let's use the elimination method:

Multiply the second equation by 5 to make the coefficients of x in both equations equal:

40x + 40y = 320

Now subtract the first equation from the second equation:

(40x + 40y) - (5x + 10y) = 320 - 70

35x + 30y = 250

Now we have a new system of equations:

35x + 30y = 250 and 5x + 10y = 70

Next, multiply the second equation by 7 to make the coefficients of y in both equations equal:

35x + 70y = 490

Now subtract the first equation from the second equation:

(35x + 70y) - (35x + 30y) = 490 - 250

40y = 240

Divide both sides of the equation by 40:

y = 6

Substitute the value of y back into the first equation:

5x + 10(6) = 70

5x + 60 = 70

5x = 10

Divide both sides of the equation by 5:

x = 2

The solution to the system of equations is (2, 6), so the correct answer is (2, 6).