If x=0 represents 2012 and x=5 represents 2017, the number of subscribers y (in millions) to the two services can be modeled by the linear equations in the following system. Solve this system. Express values as decimals rounded to the nearest tenth. Write the solution set with an ordered pair of the form (year, number of subscribers).

Question

If x=0 represents 2012 and x=5 represents​ 2017, the number of subscribers y​ (in millions) to the two services can be modeled by the linear equations in the following system. Solve this system. Express values as decimals rounded to the nearest tenth. Write the solution set with an ordered pair of the form​ (year, number of​ subscribers).
Service​ A: −5.63x+y=23.8
Service​ B: 0.71x+y=52.2

GPT 3.5 · Answer

To solve the system of linear equations, we can use substitution or elimination method.

We'll use the elimination method to solve the system.

Let's multiply the second equation by -5.63 to make the x coefficients equal:

-5.63 * (0.71x + y) = -5.63 * 52.2
-4x - 5.63y = -294.126

Now we'll write the system of equations:

-5.63x + y = 23.8
-4x - 5.63y = -294.126

To eliminate y, let's add the two equations together:

(-5.63x + y) + (-4x - 5.63y) = 23.8 + (-294.126)
-9.63x - 4.63y = -270.326

Now we have a new equation:

-9.63x - 4.63y = -270.326

Let's multiply the first equation by -4.63 to make the y coefficients equal:

-4.63 * (-5.63x +y) = -4.63 * 23.8
23.8x - 4.63y = -110.994

Now we'll write the system of equations:

23.8x - 4.63y = -110.994
-9.63x - 4.63y = -270.326

Now we will eliminate y by adding the two equations together:

(23.8x - 4.63y) + (-9.63x - 4.63y) = -110.994 + (-270.326)
14.17x - 9.26y = -381.32

Now we have a new equation:

14.17x - 9.26y = -381.32

Let's solve this equation for x:

14.17x = 9.26y - 381.32
x = (9.26y - 381.32) / 14.17

We can substitute this expression for x into one of the original equations and solve for y. Let's use the second equation:

0.71x + y = 52.2
0.71((9.26y - 381.32) / 14.17) + y = 52.2

Now let's solve this equation for y:

0.71 * (9.26y - 381.32) + 14.17y = 52.2 * 14.17
6.5796y - 270.6352 + 14.17y = 738.534

Combine like terms:

20.7496y - 270.6352 = 738.534

Now let's isolate y:

20.7496y = 739.8762
y = 739.8762 / 20.7496
y ≈ 35.7

Now we can substitute this value for y back into the expression for x:

x = (9.26(35.7) - 381.32) / 14.17
x ≈ -3.1

Therefore, the solution to the system of equations is approximately (x, y) = (-3.1, 35.7), which can be written as (-3.1, 35.7) as an ordered pair representing the year and number of subscribers.