Solving Linear Systems of Equations - Concept

• Consider the following set of equations:

8y2x4

1y2x3

• Such a set is called a Linear System of Equations in two variables. Note that both variables in both equations are degree one (exponent of 1), thus the name linear.

• Take just the first equation by itself.

1y2x3

• Find some ordered pairs that satisfy the equation.

(-1, -1)( 0, 1/2)( 1, 2)

(2, 7/2)• Each ordered pair that satisfies the equation is called a solution of the equation.

• Solutions to the second equation could be found in the same way.

8y2x4

• Now consider again the system of equations. 8y2x4

1y2x3

• The solution to the system of equations is any ordered pair ( a, b) that satisfies both equations.

x = 1 ( 1, 2) ( 1, 2)x = 1 ( 1, 2) ( 1, 2)

1y2x3 8y2x4

x-value of point First Equation Second Equation

x = - 1 (-1, -1) (-1, 6)

x = 0 ( 0, 1/2) ( 0, 4)

x = 2 ( 2, 7/2) ( 2, 0)

• Notice that ( 1, 2) is the only ordered pair that is a solution for both equations.

• Thus, ( 1, 2) is a solution to the system of equations.