Solution of Equation

Many algebraic equations contain more than one variable, so the complete solution set can not be found using the methods described thus far. Equations with two unknowns are called linear equations and can be represented by the general formula ax + by = c; where a, b, and c are constants and x and y are variables. The solution of this type of equation would be the ordered pair of x and y which makes the equation true. For example, the solution set for the equation x + y = 7 would contain all the pairs of values for x and y which satisfy the equation, such as (2,5), (3,4), (4,3) etc. In general, to determine the solution to a linear equation with two variables, the equation is rewritten and solved in terms of one variable. The solution for the equation x + y = 7, then becomes any pair of values which makes x = 7 - y true.

Often multiple linear equations exist which relate two variables in the same system. All of the equations related to the variables are known as a system of equations and their solution is an ordered pair which makes every equation true. These equations are solved by methods of graphing, substitution, and elimination.