Solve {l}{y=-{(1/3)}}{z={(3/2)}^-2*{(2/3)}^-3}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = -{(\frac{1}{3})} }\\ { z = {(\frac{3}{2})} ^ {-2} \cdot {(\frac{2}{3})} ^ {-3} }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, z, a

$$a = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Solution Steps

Consider the second equation. Calculate \frac{3}{2} to the power of -2 and get \frac{4}{9}.

$$z=\frac{4}{9}\times \left(\frac{2}{3}\right)^{-3}$$

Calculate \frac{2}{3} to the power of -3 and get \frac{27}{8}.

$$z=\frac{4}{9}\times \frac{27}{8}$$

Multiply \frac{4}{9} and \frac{27}{8} to get \frac{3}{2}.

$$z=\frac{3}{2}$$

Consider the third equation. Insert the known values of variables into the equation.

$$a=\frac{3}{2}$$

The system is now solved.

$$y=-\frac{1}{3} z=\frac{3}{2} a=\frac{3}{2}$$