The substitution method for solving linear systems

A way to solve a linear system algebraically is to use the substitution method. The substitution method functions by substituting the one y-value with the other. We're going to explain this by using an example.

 \begin{cases} y=2x+4 \\ 3x+y=9 \end{cases}  

We can substitute y in the second equation with the first equation since y = y.


$$3x+\left ( {\color{green} {2x+4}} \right )=9$$




This value of x can then be used to find y by substituting 1 with x e.g. in the first equation


$$y=2\cdot {\color{green} 1}+4$$


The solution of the linear system is (1, 6).

You can use the substitution method even if both equations of the linear system are in standard form. Just begin by solving one of the equations for one of its variables.

Video lesson

Solve the linear system using the substitution method

\begin{cases} 2y - 4x = 2\\ y = -x + 4\end{cases}