Solving a Linear System in Three Variables with no or Infinite Solutions - Concept

Concept Concept (1)

Sometimes we have a system of equations that has either infinite or zero solutions. We call these no solution systems of equations. When we solve a system of equations and arrive at a false statement, it tells us that the equations do not intersect at a common point. One scenario is that 2 or more of the planes are parallel or that two of the planes intersect and the other intersects at a different point.

Sample Sample Problems (3)

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Solving a Linear System in Three Variables with no or Infinite Solutions - Problem 1

Solve:

2a − 4b + 6c = 5
-a + 3b − 2x = -1
a − 2b + 3c = 1
Problem 1
How to solve a system of linear equations in three variables that yields no solution.
Solving a Linear System in Three Variables with no or Infinite Solutions - Problem 2

Solve:

3x − 12y + 15z = 9
x − 4y + 5z = 3
-2x + 8y − 10z = -6
Problem 2
How to solve a system of linear equations in three variables that yields the same plane.
Solving a Linear System in Three Variables with no or Infinite Solutions - Problem 3
Problem 3
3 x 3 systems with no solution or infinite solutions, solved by hand using elimination.