Solve {l}{{(3)}+x/6=1+5x/12}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { {(3)} + \frac{x}{6} = 1 + \frac{5 x}{12} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=8$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 12, the least common multiple of 6,12.

$$36+2x=12+5x$$

Subtract 5x from both sides.

$$36+2x-5x=12$$

Combine 2x and -5x to get -3x.

$$36-3x=12$$

Subtract 36 from both sides.

$$-3x=12-36$$

Subtract 36 from 12 to get -24.

$$-3x=-24$$

Divide both sides by -3.

$$x=\frac{-24}{-3}$$

Divide -24 by -3 to get 8.

$$x=8$$

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

$$y=8$$

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

$$z=8$$

The system is now solved.

$$x=8 y=8 z=8$$