Graph each equation. Which point is the solution to the system of equations?
After 3.5 weeks, 185 tickets were sold.
Practice makes perfect
We want to find out how long it will take for the festivals to sell the the same number of tickets, then find that number of tickets. We will do these things one at a time. First, let's take a look at the given system of equations, where y represents the number of tickets sold after x weeks.
&y=10x+150 &Country Music Festival &y=20x+115 &Pop Music Festival
We can solve this problem by graphing both equations on the coordinate plane and looking for a point of intersection. We know that the point of intersection of two graphs is a solution to the system of linear equations. This will be the time when the same number of tickets have been sold for both festivals. Let's do it!
The graphs seem to intersect at the point (3.5,185). This means that after 3.5 weeks, the same number of tickets have been sold for both festivals. Finally, we will check if this point is a solution to the system of equations we created. Let's substitute 3.5 for x and 185 for y in each equation and check if they hold true.
