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# System of linear equations with two unknowns

## WHAT IS IT ?

A system of linear equations with two unknowns is a mathematical model that consists of two linear equations containing two unknown variables. These variables are usually denoted as x and y. Such a system has the general form:

a1x + b1y = c1
a2x + b2y = c2

where x and y are unknown variables and a1, b1, c1, and c2 are constants. The solution to this system of equations represents a pair of values x and y that satisfy both equations simultaneously. Various methods are used to solve this system, such as the substitution method, elimination method, or graphical method.

These equations are used in many fields, such as physics, engineering, economics, and everyday problems where it is necessary to find the relationship between two variables.

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x + y =
x + y =

## EXAMPLE:

Let's consider the system of equations:

## 2x - y = 4

Let's solve this system using the substitution method:

Step 1: Express one unknown from one equation.
From the first equation, we express y:
y = 7 - x
Step 2: Substitute the expression for y into the second equation.
Substitute this expression into the second equation:
2x - (7 - x) = 4
Step 3: Solve the equation with one unknown.
Now we have an equation with only x:
2x - 7 + x = 4
3x - 7 = 4
3x = 11
x = 11/3
Step 4: Substitute the value of x back into the first equation.
Now substitute the value of x into the expression for y:
y = 7 - 11/3
y = 21/3 - 11/3
y = 10/3
So the solution to the system of equations is:
x = 11/3, y = 10/3

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