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=
To solve the system of equations, we need to solve for x and y. Let's solve for y in each equation first.
For Service A, we have:
-5.63x + y = 23.8
To solve for y, we can add 5.63x to both sides of the equation:
y = 5.63x + 23.8
For Service B, we have:
0.71x + y = ?
To solve for y, we can subtract 0.71x from both sides of the equation:
y = -0.71x + ?
Now let's find the value of "?" for Service B. We are given that x=0 represents 2012 and x=5 represents 2017.
For x=0 (2012):
0.71(0) + y = ?
0 + y = ?
y = ?
For x=5 (2017):
0.71(5) + y = ?
3.55 + y =?
y = ?
To find the values of y for x=0 and x=5, we will use the given equations. Let's substitute these values into the equations:
For Service A, when x=0:
y = 5.63(0) + 23.8
y = 0 + 23.8
y = 23.8
For Service A, when x=5:
y = 5.63(5) + 23.8
y = 28.15 + 23.8
y = 51.95
For Service B, when x=0:
y = -0.71(0) + ?
y = 0 + ?
y = ?
For Service B, when x=5:
y = -0.71(5) + ?
y = -3.55 + ?
y = ?
Now we have the values of y for each equation when x=0 and x=5.
Service A:
(2012, 23.8)
(2017, 51.95)
Service B:
(2012, ?)
(2017, ?)
To find the values of y for Service B, we will need more information or another equation. Without additional information, we cannot solve for the values of y and therefore cannot determine the solution set with an ordered pair for Service B.
To solve the system of linear equations, we need to substitute the given values of x=0 and x=5 into the equations and solve for y.
For Service A:
-5.63x + y = 23.8
Substituting x=0:
-5.63(0) + y = 23.8
0 + y = 23.8
y = 23.8
So, for Service A, when x=0 (representing 2012), y=23.8 million subscribers.
Substituting x=5:
-5.63(5) + y = 23.8
-28.15 + y = 23.8
y = 23.8 + 28.15
y = 52.95
So, for Service A, when x=5 (representing 2017), y=52.95 million subscribers.
Now let's solve for Service B:
0.71x + y = ?
Substituting x=0:
0.71(0) + y = ?
0 + y = ?
y = ?
We don't have enough information to solve for y for Service B as the equation is incomplete. Please provide the missing value in the equation for Service B.
To solve the system of linear equations, we need to find the values of x and y that satisfy both equations simultaneously. We can do this by using the method of substitution.
Let's start with the first equation:
-5.63x + y = 23.8
We'll solve this equation for y in terms of x:
y = 5.63x + 23.8
Now let's substitute this expression for y in the second equation:
0.71x + (5.63x + 23.8) = ?
Simplifying the equation, we combine like terms:
6.34x + 23.8 = ?
Next, subtract 23.8 from both sides to isolate the term with x:
6.34x = ? - 23.8
We need to determine the value of "?" to proceed with the calculation. The question doesn't provide it, so I'll assume it's a constant value. Let's call it c.
6.34x = c - 23.8
Now, to solve for x, divide both sides of the equation by 6.34:
x = (c - 23.8) / 6.34
Since we're interested in finding the solution for the given system of equations, we'll substitute the known values for x:
x = (5 - 23.8) / 6.34
Calculating the value:
x = -18.8 / 6.34 = -2.97 (rounded to the nearest tenth)
Now that we have the value of x, we can substitute it back into either of the original equations to find the corresponding value of y.
Using the first equation:
-5.63x + y = 23.8
Substituting x = -2.97:
-5.63(-2.97) + y = 23.8
Calculating:
16.7283 + y = 23.8
Subtracting 16.7283 from both sides:
y = 23.8 - 16.7283 = 7.0717 (rounded to the nearest tenth)
Therefore, the solution to the system of equations is:
(x, y) = (-2.97, 7.1)
This means that in the year represented by x = -2.97 (approximately 2010), Service A had around 7.1 million subscribers.