Chapter 6.5, Problem 49MR

To determine

To tell: whether the given system has one solution, infinitely many solutions or no

solution.

Explanation of Solution

Given information:

The given system is

  $\begin{array}{l}x+y=11\\ x+y=16\end{array}$

Find the intercepts of the equations and then draw the lines.

Consider the line $x+y=11$

  $\begin{array}{l}y=0\Rightarrow x=11\\ x=0\Rightarrow y=11\end{array}$

Consider the line $x+y=16$

  $\begin{array}{l}y=0\Rightarrow x=16\\ x=0\Rightarrow y=16\end{array}$

Graph:

The graph of given system is shown below.

  

The point of intersection of the lines of the given system is the solution of the system.

Hence, the system has no solution.