Chapter 9.2, Problem 31WE

To determine

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

Answer to Problem 31WE

The system of equation has no solution.

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}5y-2x=3\\ 6x=15y-1\end{array}$

The given equation can be written as,

  $\begin{array}{l}6x=15y-1\\ x=\frac{15y-1}{6}\end{array}$

The another given equation is,

  $5y-2x=3$

Substitute $\frac{15y-1}{6}$ for $x$ .

  $\begin{array}{l}5y-2x=3\\ 5y-2\left(\frac{15y-1}{6}\right)=3\\ 5y-\frac{15y-1}{3}=3\\ \frac{15y-15y+1}{3}=3\\ 1=9\end{array}$

Since L.H.S is not equal to R.H.S hence the following system of equation has no solution.

Thus, the system has no solution.