Chapter 6.2, Problem 38PFA

To determine

To find: Number of solutions possible for given system of equations .

Answer to Problem 38PFA

Number of solutions possible = 1

  $\begin{array}{l}x=0\\ y=0\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}x+2y=0\\ 2x=y\end{array}$

  $x+2y=0$ -----(1)

  $2x=y$

  $\Rightarrow y=2x$ ------(2)

Substitute the value of y from equation-(2) in equation-(1)

We get

  $\begin{array}{l}x+2y=0\\ \Rightarrow x+2\left(2x\right)=0\\ \Rightarrow x+4x=0\\ \Rightarrow 5x=0\\ \Rightarrow x=0\end{array}$

Substitute value of $x$ in equation-(2)

We get

  $\begin{array}{l}y=2x\\ \Rightarrow y=2\left(0\right)\\ \Rightarrow y=0\end{array}$

Therefore, values of x and y are

  $\begin{array}{l}x=0\\ y=0\end{array}$

Only one solution is possible.