To solve problems with multiple unknowns, we use the method of equations. We can set up two equations relating the unknowns, with one equation for each independent relationship between the variables. For example, if trying to determine the number of three-person and four-person seats in a bank with 40 total seats and 146 total people, we can set up equations for the number of seats equaling 40 and the number of people equaling 146. Solving the two equations simultaneously using substitution or another method provides the values of the unknowns.

1. To which method do we apply in order to reach a solution in case
more than one unknown is presented in a problem?
One of the mathematical procedure is to equate and benefit from
the solution of this equate.
The method and solution of Equation
with two unknowns of the first degree

2. In the event that the first unknown is ‘x’ and the second
unknown is ‘y’ an equate based on these unknowns is set
called ‘equation with two unknowns of the first degree.’
Let’s exemplify it.

3. In a bank there are 40 seats and some of these
banks are threesome and the left are foursome.
Because up to 146 people can use seats, how many
of these seats are threesome and foursome ?

4. As indicated in this problem there are two
unknowns.
The number of foursome seats is the first unknow
and ıt is called ‘x’
The number of the threesome seats is the second
unknown and ıt is called ‘y’ and
because the total number of seats are 40
x+y= 40
By the way :
On a foursome seat 4x1= 4 people and
On a threesome seat 3x1=3 people can sit.
In total 4x+3y=146 people can sit in the park.

5. The equations set above as x+y=40 and 4x+3y= 146
form equation method. In the event of finding both
two unknowns the problem is solved.
The solution of these equations can be reached by
three ways. These ways are :
1) Eliminate method
2) Substitution method
3) Graphical method
Substitution method in this problem will ease the
solution.

6. So;
In the equation of x+y=40, depending on ‘x’ the
number of ‘y’ is y=40-x and provided we substitute
the y with x and replace to second unknown
equation we can reach the solution.
4x+3.(40-x)=146
4x+120-3x=146
x+120=146
x=26

7. On writing this found 26 instead of x in both
unknowns ‘y’ can be reached easily.
26+y=40
y=14
So the number of foursome seats are x= 26 and
threesome seats are y=14