The substitution method is one approach to solving systems of linear equations, which involves substituting the value of one variable from one equation into the other equation. Let's consider the following example to understand the concept better:

Example:

Solve the system of equations:

Equation 1: 2x + y = 8 Equation 2: x - y = 2

To start, solve Equation 2 for x: x = 2 + y. Now substitute this value of x into Equation 1:

2(2 + y) + y = 8

By simplifying, we get:

4 + 2y + y = 8

Combining like terms, we have:

3y = 4

Dividing both sides by 3, we find that y = 4/3.

Substitute this value of y into x = 2 + y:

x = 2 + (4/3)

By simplifying, we get:

x = 10/3.

Thus, the solution to the system of equations is x = 10/3 and y = 4/3.

Note: The substitution method can be used for systems of equations with two variables. For systems with more than two variables, other methods such as elimination or matrices may be more suitable.

Remember, practice makes perfect. Try solving more systems of equations using the substitution method to strengthen your understanding!