Inconsistent and Consistent Systems

Consistent or Inconsistent?

• Consistent

• Inconsistent

What is the solution to this system of equations?

• (1,0)

• (-3, -1)

• (-1,-3)

• (1,3)

What is the solution to this system of equations?

• (1,4)

• (4,1)

• (3,5)

• (-1, 4)

Consistent or Inconsistent?

• Consistent

• Inconsistent

A system of equations with no ordered pair that satisfies both equations.

• consistent

• inconsistent

• elimination

• system of equations

Consider the system of equations 3x + 4y = 0 -3x +-4y = 2 Adding the two equations side-by-side and simplifying yields 0 = 2. Which of the following can be concluded about the system of equations?

• It has a unique solution (2, 0).

• It has exactly two solutions (2, 0) and (0, 2).

• It has infinitely many solutions.

• It has no solution.

Answer explanation

Since both sides of the equation do not equal each other, this is how you can tell that a problem has no solution.

Consider the system of equations 3x + 4y = 0 -3x +-4y = 2 Adding the two equations side-by-side and simplifying yields 0 = 2. Which of the following can be concluded about the system of equations?

• It has a unique solution (2, 0).

• It has exactly two solutions (2, 0) and (0, 2).

• It has infinitely many solutions.

• It has no solution.

Answer explanation

Since both sides of the equation do not equal each other, this is how you can tell that a problem has no solution.

Which of the following systems has no solution?

• 1. 2x – 4y = 8

  -2x + 4y = -8

• 1. 2x – 4y = 6

  -3x – 6y = 9

• 1. 2x + 4y = 8

  -3x – 6y = -9

• 1. 3x – 6y = 9

  3y – 6x = 9

Which system of equations has no solution?

When there is one or infinite solutions it is called

• Inconsistent system

• Consistent System