Chapter 6, Problem 16SGR

To determine

To graph:

The following equations of system and the set of solution:

  $\begin{array}{l}3x+y=5\\ 6x=10-2y\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}3x+y=5\\ 6x=10-2y\end{array}$

Graph:

  

Interpretation:

The given system of equation is:

  $3x+y=5$

… (1)

  $\begin{array}{l}6x=10-2y\\ 6x+2y=10\\ 2\left(3x+y\right)=10\end{array}$

  $3x+y=5$

… (2)

The two equations represented eq. (1) and (2) are same. That’s why get a single line as graph of two equations. When a graph of two equations gives a same line of graph, it contains the infinite number of solutions.

Therefore, infinite number of solutions is observed for given system of equation.