How to Solve a System of Linear Equations by Substitution

When dealing with a system of linear equations in algebra, substitution is a handy technique. Let's consider the system

[ \begin{align*} 2x + y &= 8 \ 3x - y &= 4 \end{align*} ]

First, solve one equation for one variable, for example, solve the second equation for (y), getting (y = 3x - 4). Then, substitute this expression for (y) in the first equation. This gives you (2x + (3x - 4) = 8). Simplify and solve for (x). Once you find the value of (x), substitute it back into either of the original equations to find the value of (y).

By following this method, you can easily solve a system of linear equations by substitution.