Write a system of equations for the following situation: A group of 10 people went to see a movie.?

"A group of 10 people went to see a movie."

"The cost to go to the movie is $8 for an adult and $5 for a child. The total cost for the group was $59"

8a + 5c = 59
a + c =10

You have two lines. Where they cross, the values of x and y satisfy both equations simultaneously, so it is called a simultaneous system. There are two ways to find that point. Substitution is when you solve one equation for one variable and substitute that into the other equation.

a = 10 - c Substitute this for a in the other equation.
8(10 - c) + 5c = 59
-3c = -21
c = 7 Put this into either original equation to find the value of a.
a = 3

Elimination is when you add the equations in a way to eliminate one variable. Otherwise the process is the same.

8a + 5c = 59
-8a - 8c =-80
---------------- ADD
0 -3c = -21
c = 7 <-- SAME ANSWER