Solve {l}{x+27=y}{27-3y=3}{x+z=y}

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

Solve for x, y, z

$$x=-19$$

$$y=8$$

$$z=27$$

Solution Steps

Consider the second equation. Subtract 27 from both sides.

$$-3y=3-27$$

Subtract 27 from 3 to get -24.

$$-3y=-24$$

Divide both sides by -3.

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

Divide -24 by -3 to get 8.

$$y=8$$

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

$$x+27=8$$

Subtract 27 from both sides.

$$x=8-27$$

Subtract 27 from 8 to get -19.

$$x=-19$$

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

$$-19+z=8$$

Add 19 to both sides.

$$z=8+19$$

Add 8 and 19 to get 27.

$$z=27$$

The system is now solved.

$$x=-19 y=8 z=27$$