Your equations should have the number of songs dependent on the number of years that have passed.
System of equations: s=6t+24 s=12t Graph:
Solution: They will have written the same number of songs after four years.
Practice makes perfect
First, let's define our variables. We need to know the number of songs s that have been written as a function of the number of years t that have passed. We are told that Jay has already written 24 songs and will continue to average an additional 6 songs each year. Let's write this as an equation.
s=24+6 t
Jenna, on the other hand, has just started writing songs but is expecting to average 12 songs per year. This too we can write as an equation.
s=12 t
Combining these, we get the following system of equations.
s=24+6 t & (I) s=12 t & (II)
We can solve this system of equations graphically by graphing both lines and see where they intersect. When graphing the lines we want both functions written in slope-intercept form. Therefore, we need to rewrite Equation (I).
s=24+6 t s=12 t ⇔ s=6 t+24 s=12 t
Let's graph Equation (I), which tells us how many songs Jay has written. We will use that the graph intercepts the vertical axis at 24 and that its slope is 6. When graphing we must keep in mind that we cannot have a negative number of songs.
Now let's add Jenna's graph to the same coordinate plane. Jenna's function intercepts the vertical axis at 0 and has a slope of 12.
Looking at the two functions graphed together, we can see that they intersect at t=4.
This tells us that they will have written the same number of songs after four years.
