AUse the information from the exercise to create two equations and then combine them into a system.
BUse the Substitution Method to solve the system of equations created in Part A.
Ax+y=64 & (I) x=y+14 & (II)
BThere are 39 students in the filmmaking club and 25 students in the yearbook club.
Practice makes perfect
We want to create a system of linear equations to represent the number of students in a filmmaking club and a yearbook club. Let's use x to represent the number of students in the filmmaking club and y to represent the number of students in the yearbook club. From the exercise we know that there are a total of 64 students in these two clubs.
x+ y= 64
We also know that there are 14 more students in the filmmaking club than in the yearbook club.
x= y+ 14
Now we can create our system of equations. Let's combine the two equations we created and make them into one system.
x+y=64 & (I) x=y+14 & (II)
We want to know how many students are in the filmmaking club and the yearbook club. We can find this information by solving the system of equations we created in Part A. Let's take another look at it.
x+y=64 & (I) x=y+14 & (II)
To solve this system we will use the Substitution Method. Notice that Equation (II) is already solved for x. Because of this, we will substitute y+14 for x in Equation (I) and solve it for y. Let's do it!
Now that we have a value for y, we can substitute its value for y in either equation and solve for x. Let's substitute 25 for y in Equation (II) for simplicity.
