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?