Chapter 6, Problem 14CR

To determine

To solve the system of equations $\begin{array}{l}2x+y=-12\\ -4x-2y=30\end{array}$ by using the method of substitution.

Answer to Problem 14CR

No solution.

Explanation of Solution

Given:

  $\begin{array}{l}2x+y=-12\\ -4x-2y=30\end{array}$

Calculation:

  $\begin{array}{l}2x+y=-12\to \left(1\right)\\ -4x-2y=30\to \left(2\right)\end{array}$

From equation (1), we have

  $\begin{array}{l}2x+y=-12\\ \Rightarrow y=-2x-12\end{array}$

Now substituting $y=-2x-12$ in equation (2), we get

  $\begin{array}{l}-4x-2\left(-2x-12\right)=30\\ \Rightarrow -4x+4x+24=30\\ \Rightarrow 24=30\end{array}$

Which is not possible.

Hence the given system of equations has no solution.