# Algebraic Method

## DEFINITION of 'Algebraic Method'

A mathematical means of solving a pair of linear equations. Algebraic method refers to a method of solving an equation involving two or more variables where one of the variables is expressed as a function of one of the other variables. There are typically two algebraic methods used in solving these types of equations: the substitution method and the elimination method.

## BREAKING DOWN 'Algebraic Method'

One algebraic method is the substitution method. In this case, the value of one variable is expressed in terms of another variable and then substituted in the equation. In the other algebraic method – the elimination method – the equation is solved in terms of one unknown variable after the other variable has been eliminated by adding or subtracting the equations. For example, to solve:

8x + 6y = 16

-8x – 4y = -8

Using the elimination method, one would add the two equations as follows:

8x + 6y = 16

-8x – 4y = -8

2y = 8

y = 4

The variable "x" has been eliminated. Once the value for y is known, it is possible to solve for x by substituting the value for y in either equation:

8x + 6y = 16

8x + 6(4) = 16

8x + 24 = 16

8x + 24 – 24 = 16 – 24

8x = -8

X = - 1