Chapter 6.2, Problem 40PPE

To determine

To calculate: Will the given system always, sometimes or never have a solution.

Answer to Problem 40PPE

Never.

Explanation of Solution

Given information:

  $\begin{array}{l}y=ax\\ y=ax+4\end{array}$

Let $a$ be any real number.

Calculation:

Both the equations of the system have same slope, i.e. $a$ . Now, if two lines have same slope, that means they two are parallel lines. Parallel lines do not intersect at all. Here our equations are equations of parallel lines which do not intersect anywhere. As system do not intersect anywhere, the systems will never have a solution.