Question

in the music industry, revenue from sales of cds has been declining in recent years, while the revenue from sales of vinyl records has been increasing. for the years 2013 through 2020, the revenue (in millions of dollars) from the sale of cds is approximated by the equation y = - 235x + 1853.5, while for vinyl records, the equation is y = 44x + 458.5, where x is the number of years after 2013. a. use the substitution method to solve this system of equations. b. explain the meaning of the solution of the system. c. sketch a graph of the system of equations. write a sentence describing the trends for revenue from sales of cds and vinyl records. the solution of the system is (type an ordered - pair using integers or decimals.)

Explanation:

Step1: Set up the system of equations

We have the system: $y=- 235x + 1853.5$ (CD - revenue) and $y = 44x+458.5$ (vinyl - revenue)

Step2: Substitute one equation into the other

Since both equations are equal to $y$, we set $-235x + 1853.5=44x+458.5$

Step3: Solve for $x$

First, add $235x$ to both sides: $1853.5=44x + 235x+458.5$. Then combine like - terms: $1853.5=279x+458.5$. Subtract $458.5$ from both sides: $1853.5 - 458.5=279x$, so $1395 = 279x$. Divide both sides by $279$: $x=\frac{1395}{279}=5$

Step4: Solve for $y$

Substitute $x = 5$ into $y = 44x+458.5$, then $y=44\times5+458.5=220 + 458.5=678.5$

Answer:

$(5,678.5)$