Solve {l}{x/0.3-1.5-2x/0.2=1}{y=x-0.3{(1.5-2x)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{x}{0.3} - \frac{1.5 - 2 x}{0.2} = 1 }\\ { y = x - 0.3 {(1.5 - 2 x)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=0.57$$

Short Steps Using Substitution

Reorder the equations.

$$y=x-0.3\left(1.5-2x\right) \frac{x}{0.3}-\frac{1.5-2x}{0.2}=1 z=y$$

Calculate y from y=x-0.3\left(1.5-2x\right).

$$y=1.6x-0.45$$

Substitute 1.6x-0.45 for y in the equation z=y.

$$z=1.6x-0.45$$

Solve \frac{x}{0.3}-\frac{1.5-2x}{0.2}=1 for x.

$$x=\frac{51}{80}$$

Substitute \frac{51}{80} for x in the equation z=1.6x-0.45.

$$z=1.6\times \frac{51}{80}-0.45$$

Calculate z from z=1.6\times \frac{51}{80}-0.45.

$$z=\frac{57}{100}$$

Substitute \frac{51}{80} for x in the equation y=1.6x-0.45.

$$y=1.6\times \frac{51}{80}-0.45$$

Calculate y from y=1.6\times \frac{51}{80}-0.45.

$$y=\frac{57}{100}$$

The system is now solved.

$$x=\frac{51}{80} y=\frac{57}{100} z=\frac{57}{100}$$