Chapter 6, Problem 16CR

To determine

To solve the system of equations $\begin{array}{l}y=x-7\\ 3x-3y=21\end{array}$ by using the method of substitution.

Answer to Problem 16CR

Infinite solutions.

Explanation of Solution

Given information:

  $\begin{array}{l}y=x-7\\ 3x-3y=21\end{array}$

Calculation:

  $\begin{array}{l}y=x-7\to \left(1\right)\\ 3x-3y=21\to \left(2\right)\end{array}$

Now substituting equation (1) in equation (2), we get

  $\begin{array}{l}3x-3\left(x-7\right)=21\\ \Rightarrow 3x-3x+21=21\\ \Rightarrow 21=21\end{array}$

Hence the given system of equations has infinite solutions.