Systems of Equations with Special Cases (5.4)
Infinitely many solutions
Solve the system of linear equations y = -4x + 2 4x + y = 2
No Solution
Solve the system of linear equations y = 2x + 5 y = 2x - 7
(-1,-8)
Solve the system of linear equations using elimination 8x + 6y = -16 -3x +6y = -5
(10,-1)
Solve the system of linear equations using elimination x - 2y = 11 2x + 2y = 19
(4,3)
Solve the system of linear equations using substitution 2x - 3y = -1 y = x - 1
(2,3)
Solve the system of linear equations using substitution y = 5x - 7 -3x - 2y = -12
(5,10)
Solve the system of linear equations using substitution y = x + 5 3x + y = 25
It is a true statement. For example, 2=2 is a true statement.
How can you tell if equations have infinitely many solutions algebraically?
Same slope and same y-intercept
How can you tell if equations have infinitely many solutions?
It is a false statement. For example, 5=-3 is NOT a true statement
How can you tell if equations have no solution algebraically?
Same slope and different y-intercept
How can you tell if equations have no solution?
Different slope
How can you tell if equations have one solution?
Infinitely Many Solutions (graph)
How many solutions are there in this graph?
No Solution (graph)
How many solutions are there in this graph?
One Solution (graph)
How many solutions are there in this graph?