What does k not equal to if the following system is consistent?

{(-6x-12y=3),(kx-24y=9):}

 

Expert Answers

An illustration of the letter 'A' in a speech bubbles

A system of equations is consistent if it has a solution. The equations -6x-12y=3 and kx-24y=9 represent two straight lines. The solution is the coordinates of the point where the lines intersect.

Two lines do not intersect only of they are parallel to each other. This is the case if they have an equal slope.

The slope of -6x - 12y = 3 is -6/12 = -1/2. If the line kx-24y=9 has a slope -1/2, the value of k is -12.

The system of equations is consistent for all values of k except k = -12.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial