The system of equations 3x + by + c = 0 and ax - 8y + 9 = 0 does not have any solution. What are the possible values of a and b.

Expert Answers

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

Each of the equations in the given system of equations represents a straight line. The solution of the system of equations is the point at which the lines intersect.

The system of equations does not have a solution if the two lines are parallel to each other. They can be expressed in the slope intercept form as follows:

3x + by + c = 0

=> `y = (-3/b)x - c/b`

ax - 8y + 9 = 0

=> `y = (a/8)x + 9/8`

The slope of the lines is equal if `-3/b = a/8 => a*b = -24` .

a and b can take on an infinite number of values for which the given equations do not have a solution. The product a*b should be equal to -24.

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial