In mathematics, systems of linear equations arise when we have multiple linear equations that need to be solved simultaneously. The solution to a system of linear equations is the set of values that satisfy all the equations in the system. Let's look at a simple example to understand how to solve a system of linear equations.

Suppose we have the following system of equations:

2x + 3y = 11
4x - y = 5

To solve this system, we can use different methods such as substitution, elimination, or graphing. Let's use the substitution method in this example.

Step 1: Solve one equation for one variable

We can solve the second equation for y in terms of x. Solving for y, we get:

y = 4x - 5

Step 2: Substitute the expression for the variable into the other equation

Substitute the value of y in terms of x into the first equation:

2x + 3(4x - 5) = 11

Step 3: Simplify and solve for x

Now, we can simplify the equation and solve for x:

2x + 12x - 15 = 11
14x = 26
x = 26/14
x = 13/7

Step 4: Find the value of the other variable

Substitute the value of x back into one of the original equations to find the value of y:

4(13/7) - y = 5
52/7 - y = 5
y = 52/7 - 5
y = 52/7 - 35/7
y = 17/7

Thus, the solution to the system of equations is x = 13/7 and y = 17/7.