Solving Linear Systems of Equations - Concept

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

Slide 4
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Solving Linear Systems of Equations - Concept
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