Solve {l}{x+y+z=7434}{x=3/4y}{y=5/6*z}

$$\left\{ \begin{array} { l } { x + y + z = 7434 } \\ { x = \frac { 3 } { 4 } y } \\ { y = \frac { 5 } { 6 } \cdot z } \end{array} \right.$$

Solve for x, y, z

$$x=1890$$

$$y=2520$$

$$z=3024$$

Short Steps Using Substitution

Reorder the equations.

$$x=\frac{3}{4}y x+y+z=7434 y=\frac{5}{6}z$$

Substitute \frac{3}{4}y for x in the equation x+y+z=7434.

$$\frac{3}{4}y+y+z=7434$$

Solve the second equation for y and the third equation for z.

$$y=-\frac{4}{7}z+4248 z=\frac{6}{5}y$$

Substitute -\frac{4}{7}z+4248 for y in the equation z=\frac{6}{5}y.

$$z=\frac{6}{5}\left(-\frac{4}{7}z+4248\right)$$

Solve z=\frac{6}{5}\left(-\frac{4}{7}z+4248\right) for z.

$$z=3024$$

Substitute 3024 for z in the equation y=-\frac{4}{7}z+4248.

$$y=-\frac{4}{7}\times 3024+4248$$

Calculate y from y=-\frac{4}{7}\times 3024+4248.

$$y=2520$$

Substitute 2520 for y in the equation x=\frac{3}{4}y.

$$x=\frac{3}{4}\times 2520$$

Calculate x from x=\frac{3}{4}\times 2520.

$$x=1890$$

The system is now solved.

$$x=1890 y=2520 z=3024$$