Chapter 3.2, Problem 48PPS

To determine

To find: the solution of the given system of equation.

Answer to Problem 48PPS

infinitely number of solutions.

Explanation of Solution

Given:

The given system of equation is $\begin{array}{l}\frac{3}{2}y+z=-3\\ -y-\frac{2}{3}z=-2\end{array}$.

Calculation:

As the given system of equation is $\begin{array}{l}\frac{3}{2}y+z=-3\\ -y-\frac{2}{3}z=-2\end{array}$.

Since none of the expressions is same on both the equation, therefore multiply by $\frac{3}{2}$ in 2nd equation and then equate:

  $\begin{array}{l}-y-\frac{2}{3}z=-2\\ \frac{3}{2}\left(-y-\frac{2}{3}z\right)=-2\times \frac{3}{2}\\ -\frac{3}{2}y-z=-3\end{array}$

Now, add the equation

  $\begin{array}{l}\underset{\_}{\begin{array}{l}\frac{3}{2}y+z=3\\ -\frac{3}{2}y-z=-3\\ ---\end{array}}\\ 0=0\end{array}$

Thus, both the equation is coinciding, so the system is equivalent.

Hence, the value of given system of equation has infinitely number of solutions.