Chapter 6, Problem 19CR

To determine

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

Answer to Problem 19CR

No solution.

Explanation of Solution

Given information:

  $\begin{array}{l}x+2y=23\\ 5x+10y=55\end{array}$

Calculation:

  $\begin{array}{l}x+2y=23\to \left(1\right)\\ 5x+10y=55\to \left(2\right)\end{array}$

Now,

  $\begin{array}{l}\left[5\times \text{Equation}\left(\text{1}\right)\right]-\left[\text{Equation}\left(\text{2}\right)\right]\\ 5\left(x+2y\right)-\left(5x+10y\right)=5\left(23\right)-55\\ \Rightarrow 5x+10y-5x-10y=115-55\\ \Rightarrow 0=60\end{array}$

Which is not possible.

Hence the given system of equations has no solution.