Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Solving Systems of Linear Equations using Substitution

Solving Systems of Linear Equations using Substitution 1.11 - Solution

arrow_back Return to Solving Systems of Linear Equations using Substitution
a

Let nn represent the number of people in the group who are not members of the fan club and mm represent the number of members. It is given that there are 1111 people in the group. Using this information, we can write the equation n+m=11. n+m=11. It is also given that a non-member pays $18\$18 for a ticket and a member pays $13\$13 dollars, and that they together pay $178\$178 for their tickets. Using this information, we can write the equation 18n+13n=178. 18n+13n=178. Combining these equations we have the following system of equations. {n+m=1118n+13m=178\begin{cases}n+m=11 \\ 18n+13m=178 \end{cases}

b
To find how many in the group are members of the fan club and how many are not, we have to solve the system {n+m=11(I)18n+13m=178(II)\begin{cases}n+m=11 & \, \text {(I)}\\ 18n+13m=178 & \text {(II)}\end{cases} for nn and m.m. We will solve solve it using the Substitution Method. Before we can substitute, we need to isolate one of the variables in one of the equations. Let's isolate nn in Equation (I). n+m=11n=11m n+m=11 \quad \Leftrightarrow \quad n=11-m Now we can substitute 11m11-m for nn in Equation (II) and solve the resulting equation for m.m.
18n+13m=17818n+13m=178
18(11m)+13m=17818({\color{#0000FF}{11-m}})+13m=178
19818m+13m=178198-18m+13m=178
Solve for mm
1985m=178198-5m=178
-5m=-20\text{-} 5m=\text{-} 20
m=4m=4
Now that we've determined m=4,m=4, we can substitute this into either of the original equations and solve the resulting equation for n.n. For simplicity, we will use Equation (I).
n+m=11n+m=11
n+4=11n+{\color{#0000FF}{4}}=11
n=7n=7
We have found that there in the group was 44 that were members of the fan club and 77 that were not.