Types of Solutions

A System of Linear Equations means two of more linear equations.

If the two lines intersect, then the point of intersection is called the solution.

If the graphs have a solution, the system is consistent.

oIf the system has one solution, then it is consistent and independent

oIf the system has infinite solutions, then it is consistent and dependent

If the graphs do not intersect, the system has no solution and is inconsistent.

The system has exactly 1 solution. Systems have 1 and only 1 solution when the two lines have different slopes. This system is consistent and independent.

Solutions is (20, 4)

System has infinite solutionsA system of equations has infinite solutions if the two lines are exactly the same.They have the same slope and y-intercept.The system is consistent and dependent

Example Line 1: y= x +2Line 2: y= 3x + 6

If you divide line 2 by 3, It will be exactly the same as line 1

The graph of the two lines are exactly the same.

System has no solutions

System has no solutions when the lines are parallel. The equations have the same slope with different y-intercepts.The system is inconsistent.

Example Line 1: y = 2x + 1Line 2: y = 2x - 1

The lines are parallel to each other.