Given the system of equations in two variables a_1 x + b_1 y = c_1, a_2 x + b_2 y = c_2 assign possible values of a_1, b_1, c_1, a_2, b_2, c_2 to make the system consistent and dependent.

Expert Answers

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

Two equations in a system of equations are consistent and dependent when the graph of both the equations are the same and it is not possible to find a unique solution for the variables which would have been possible in case the graphs of the two equations intersected only at a single point.

Here we have to find a_1, b_1, c_1, a_2, b_2, c_2 such that a_1 x + b_1 y = c_1 and a_2 x + b_2 y = c_2 are consistent and dependent.

This is possible when a_2/a_1 = b_2/b_1 = c_2/c_1 = k which is a constant.

When the ratio of a_2 and a_1, b_2 and b_1 and c_2 and c_1 is the same the equations are consistent and dependent.

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