Chapter 6.1, Problem 35PPE

To determine

To decide: whether the given system has one solution or many solutions or no solution.

Explanation of Solution

Given information:

The given system is

  $\begin{array}{l}y=x-4\\ y=x-3\end{array}$

Consider the system of equations

  $\begin{array}{l}y=x-4\\ y=x-3\end{array}$

Compare with slope intercept form $y=mx+c$

The slope of the above two equations is same.

  $m=1$

So, the two lines are parallel to each other and there is no point of intersection.

Hence, the system has no solution.