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: −5.65x+y=23.5
Service B: 0.71x+y=52.1
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Part 1
The solution set with an ordered pair of the form (year, number of subscribers) is enter your response here.
To solve the system of equations, we can use the method of substitution or elimination.
Using the method of substitution:
1. Solve one equation for one variable in terms of the other variable. Let's solve the first equation for y:
-5.65x + y = 23.5
y = 5.65x + 23.5
2. Substitute this expression for y into the second equation:
0.71x + (5.65x + 23.5) = 52.1
3. Simplify and solve for x:
6.36x + 23.5 = 52.1
6.36x = 52.1 - 23.5
6.36x = 28.6
x = 28.6 / 6.36
x ≈ 4.5
4. Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
-5.65(4.5) + y = 23.5
-25.425 + y = 23.5
y = 23.5 + 25.425
y ≈ 48.9
The solution to the system of equations is approximately (4.5, 48.9) which represents the year and number of subscribers, respectively.
To solve the system of linear equations, we need to find the values of x (year) and y (number of subscribers) that satisfy both equations.
1. Solving for y in the first equation:
-5.65x + y = 23.5
y = 5.65x + 23.5
2. Substituting this value of y into the second equation:
0.71x + (5.65x + 23.5) = 52.1
6.36x + 23.5 = 52.1
6.36x = 52.1 - 23.5
6.36x = 28.6
x = 28.6 / 6.36
x ≈ 4.5 (rounded to the nearest tenth)
3. Substituting the value of x back into the first equation to find y:
y = 5.65(4.5) + 23.5
y = 25.425 + 23.5
y ≈ 48.9 (rounded to the nearest tenth)
Therefore, the solution set with an ordered pair of the form (year, number of subscribers) is approximately (4.5, 48.9).
To solve this system of equations, we can use the method of substitution. First, let's solve one of the equations for one variable and substitute it into the other equation.
In Service A, the equation is given as: -5.65x + y = 23.5
Solving for y, we get: y = 5.65x + 23.5
Now, substitute this value of y into Service B equation:
0.71x + (5.65x + 23.5) = 52.1
Combine like terms:
6.36x + 23.5 = 52.1
Subtract 23.5 from both sides:
6.36x = 28.6
Divide both sides by 6.36:
x = 4.5
Now substitute this value of x into either equation to find y. Let's use the equation from Service A:
y = 5.65x + 23.5
y = 5.65(4.5) + 23.5
y = 25.425 + 23.5
y = 48.925
Therefore, the solution to the system is (4.5, 48.9). This means that in the year 2016.5 (midway between 2012 and 2017), the number of subscribers to Service A was approximately 48.9 million.