Solve {l}{x+2/3{(x-3)}=4/3-5{(x-6/5)}}{y=x-3x-12}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x + \frac{2}{3} {(x - 3)} = \frac{4}{3} - 5 {(x - \frac{6}{5})} }\\ { y = x - 3 x - 12 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = -\frac{74}{5} = -14\frac{4}{5} = -14.8$$

Solution Steps

Consider the first equation. Use the distributive property to multiply \frac{2}{3} by x-3.

$$x+\frac{2}{3}x-2=\frac{4}{3}-5\left(x-\frac{6}{5}\right)$$

Combine x and \frac{2}{3}x to get \frac{5}{3}x.

$$\frac{5}{3}x-2=\frac{4}{3}-5\left(x-\frac{6}{5}\right)$$

Use the distributive property to multiply -5 by x-\frac{6}{5}.

$$\frac{5}{3}x-2=\frac{4}{3}-5x+6$$

Add \frac{4}{3} and 6 to get \frac{22}{3}.

$$\frac{5}{3}x-2=\frac{22}{3}-5x$$

Add 5x to both sides.

$$\frac{5}{3}x-2+5x=\frac{22}{3}$$

Combine \frac{5}{3}x and 5x to get \frac{20}{3}x.

$$\frac{20}{3}x-2=\frac{22}{3}$$

Add 2 to both sides.

$$\frac{20}{3}x=\frac{22}{3}+2$$

Add \frac{22}{3} and 2 to get \frac{28}{3}.

$$\frac{20}{3}x=\frac{28}{3}$$

Multiply both sides by \frac{3}{20}, the reciprocal of \frac{20}{3}.

$$x=\frac{28}{3}\times \frac{3}{20}$$

Multiply \frac{28}{3} and \frac{3}{20} to get \frac{7}{5}.

$$x=\frac{7}{5}$$

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

$$y=\frac{7}{5}-3\times \frac{7}{5}-12$$

Multiply -3 and \frac{7}{5} to get -\frac{21}{5}.

$$y=\frac{7}{5}-\frac{21}{5}-12$$

Subtract \frac{21}{5} from \frac{7}{5} to get -\frac{14}{5}.

$$y=-\frac{14}{5}-12$$

Subtract 12 from -\frac{14}{5} to get -\frac{74}{5}.

$$y=-\frac{74}{5}$$

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

$$z=-\frac{74}{5}$$

The system is now solved.

$$x=\frac{7}{5} y=-\frac{74}{5} z=-\frac{74}{5}$$