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:

a_{1}x + b_{1}y = c_{1}

a_{2}x + b_{2}y = c_{2}

where x and y are unknown variables and a_{1}, b_{1}, c_{1}, and c_{2} 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.

Let's consider the system of equations:

Let's solve this system using the substitution method:

From the first equation, we express

y = 7 - x

Substitute this expression into the second equation:

2x - (7 - x) = 4

Now we have an equation with only

2x - 7 + x = 4

3x - 7 = 4

3x = 11

x = 11/3

Now substitute the value of

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

x = 11/3, y = 10/3

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