1. Solving Linear Systems of Equations - Concept
Consider the following set of equations:
Such a set is called a Linear System of Equations in two variables. Note that both variables are degree one, thus the name linear.

2. Solving Linear Systems of Equations - Concept
Take just the first equation by itself.
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.
Slide 2

3. Solving Linear Systems of Equations - Concept
Solutions to the second equation could be found in the same way.
Now consider again the system of equations.
The solution to the system of equations is any ordered pair ( a, b) that satisfies both equations.
Slide 3

4. Solving Linear Systems of Equations - Concept
x-value of point First Equation Second Equation
x = (-1, -1) (-1, 6)
x = ( 0, 1/2) ( 0, 4)
x = ( 1, 2) ( 1, 2)
x = ( 1, 2) ( 1, 2)
x = ( 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.
Slide 4

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Solving Linear Systems of Equations - Concept
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