Solve {l}{x+2y=46}{y+3z=41}{3z=27}

$$\left. \begin{array} { l } { x + 2 y = 46 } \\ { y + 3 z = 41 } \\ { 3 z = 27 } \end{array} \right.$$

Solve for x, y, z

$$x=18$$

$$y=14$$

$$z=9$$

Solution Steps

Consider the third equation. Divide both sides by 3.

$$z=\frac{27}{3}$$

Divide 27 by 3 to get 9.

$$z=9$$

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

$$y+3\times 9=41$$

Multiply 3 and 9 to get 27.

$$y+27=41$$

Subtract 27 from both sides.

$$y=41-27$$

Subtract 27 from 41 to get 14.

$$y=14$$

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

$$x+2\times 14=46$$

Multiply 2 and 14 to get 28.

$$x+28=46$$

Subtract 28 from both sides.

$$x=46-28$$

Subtract 28 from 46 to get 18.

$$x=18$$

The system is now solved.

$$x=18 y=14 z=9$$