Inconsistent Systems

When two lines in a system do not intersect it is said to be a _______ system

• inconsistent

• consistent

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

Inconsistent Systems will have ___________.

• many solutions

• no solution

• one 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.

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.

Which of the following systems of equations has no solution?

• \[\begin{cases}x + y = 3 \\ 2x + 2y = 6\end{cases}\]

• \[\begin{cases}x - y = 2 \\ 2x - 2y = 4\end{cases}\]

• \[\begin{cases}x + y = 1 \\ x - y = 1\end{cases}\]

• \[\begin{cases}x + y = 2 \\ x + y = 3\end{cases}\]

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

The pair of linear equations 3x + 5y = 3 ; 6x + ky = 8 do not have any solutions if : 

• k = 5

• k = 10

• k ≠ 10

• k ≠ 5

Which system of equations has no solution?