Consistent System of Equations

A system of equations that has a least one solution is

• Consistent

• inconsistent

• dependent

• independent

A consistent system that has infinitely many solutions is

• dependent

• consistent

• independent

• inconsistent

A consistent system that has exactly one solution

• inconsistent

• consistent

• dependent

• independent

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many Solutions

Solve the system.

• (3, -2, 4)

• (2, -3, 1)

• (-3, 2, -1)

• Infinitely many solutions

If a pair of linear equations is consistent, then the lines will be 

•  parallel

• always coincident

• intersecting or coincident

•  always intersecting

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

The pair of linear equations:
 kx + 4y = 5 ; 3x + 2y = 5
 is consistent only when:

• k ≠ 6

• k = 6

• k ≠ 3

• x = 3

Consistent - a system that has _____

• at least one solution

• exactly one solution

• infinitely many solutions

• no solutions

How many solution does a consistent and dependent system of linear equations have?

• none

• 1

• 2

• infinite