Chapter 9.2, Problem 33WE

To determine

To find: Whether the system of equation has no solution or infinitely many solutions.

Answer to Problem 33WE

The system has infinitely many solution and three solutions are $\left(0,0\right),\left(16,2.2\right),\left(3.5,0.5\right)$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}2x=14y\\ \frac{x-y}{3}=\frac{x+y}{4}\end{array}$

The given equation can be written as,

  $\begin{array}{l}2x=14y\\ x=7y\end{array}$

The another given equation is,

  $\begin{array}{l}\frac{x-y}{3}=\frac{x+y}{4}\\ 4x-4y=3x+3y\\ x-7y=0\end{array}$

Substitute $7y$ for $x$ .

  $\begin{array}{l}x-7y=0\\ 7y-7y=0\\ 0=0\end{array}$

Since L.H.S is equal to R.H.S hence the following system of equation has infinitely many solutions.

Three solutions of the given system are $\left(0,0\right),\left(16,2.2\right),\left(3.5,0.5\right)$ .

Thus, the system has infinitely many solution and three solutions are $\left(0,0\right),\left(16,2.2\right),\left(3.5,0.5\right)$ .