Final answer:
Jay and Jenna's songwriting progress can be modeled by linear equations, with Jay's being J(x) = 24 + 6x and Jenna's being Je(x) = 12x. Solving these equations, we find that Jenna will have written as many songs as Jay in 4 years. Graphically, the intersection point of the lines represents the year when they will have an equal number of songs.
Step-by-step explanation:
The subject of the question is to solve a system of linear equations to determine in how many years Jenna will have written as many songs as Jay.
Let x represent the number of years from now. We can create two equations based on the information given. For Jay, who has already written 24 songs and writes 6 songs per year, the equation is J(x) = 24 + 6x. For Jenna, who is starting from zero and writes 12 songs per year, her equation is Je(x) = 12x.
To find when Jenna will have written as many songs as Jay, we set the two equations equal to each other: 24 + 6x = 12x. Solving this equation for x, we subtract 6x from both sides to get 24 = 6x, and then divide both sides by 6 to get x = 4. So, Jenna will have written as many songs as Jay in 4 years.
To graph these equations, we would plot the two lines y = 24 + 6x and y = 12x on a coordinate plane. The point where they intersect is the solution, (4, 48), indicating that both will have written 48 songs in 4 years.