Chapter 6, Problem 24CR

To determine

To solve the system of equations by using the method of elimination.

Answer to Problem 24CR

The given system of equations has infinite solutions.

Explanation of Solution

Given information:

  $\begin{array}{l}y=3x-27\\ x-\frac{1}{3}y=9\end{array}$

Calculation:

  $\begin{array}{l}y=3x-27\Rightarrow 3x-y=27\to \left(1\right)\\ x-\frac{1}{3}y=9\to \left(2\right)\end{array}$

Now,

  $\begin{array}{l}\left[\text{Equation}\left(\text{1}\right)\right]-\left[3\times \text{Equation}\left(\text{2}\right)\right]\\ \left(3x-y\right)-3\left(x-\frac{1}{3}y\right)=27-3\left(9\right)\\ \Rightarrow 3x-y-3x+y=27-27\\ \Rightarrow 0=0\end{array}$

Hence the given system of equations has infinite solutions.