Question

For the system of two linear simultaneous equations, Choose the appropriate statement

• A. They can be intersecting lines
• B. They can be non-intersecting and parallel lines
• C. They can be identical lines
• D. All of the above.

Answer 1

The correct option is D All of the above.

Let one line is: $y=m_{1}x+b_1$
Another line is: $y=m_{2}x+b_2$

Case 1: When $m_1\ne m_1$ and $b_1,b_2\in R$
Then lines are intersecting, they will have single solutions.

Case 2: When $m_1=m_1$ and $b_1\ne b_2$
Then lines are parallel and lines will not intersect to each others.

Case 3: When $m_1=m_1$ and $b_1=b_2$
Lines are identical and will have infinite number of solutions.