3. 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)
4. System has infinite solutions A 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 +2 Line 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.
5. 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 + 1 Line 2: y = 2x - 1 The lines are parallel to each other.