Solve {l}{y=-y}{x-y=3}{z-x=6}

$$\left. \begin{array} { l } { y = - y } \\ { x - y = 3 } \\ { z - x = 6 } \end{array} \right.$$

Solve for y, x, z

$$x=3$$

$$y=0$$

$$z=9$$

Solution Steps

Consider the first equation. Add y to both sides.

$$y+y=0$$

Combine y and y to get 2y.

$$2y=0$$

Divide both sides by 2. Zero divided by any non-zero number gives zero.

$$y=0$$

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

$$x-0=3$$

Multiply -1 and 0 to get 0.

$$x+0=3$$

Anything plus zero gives itself.

$$x=3$$

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

$$z-3=6$$

Add 3 to both sides.

$$z=6+3$$

Add 6 and 3 to get 9.

$$z=9$$

The system is now solved.

$$y=0 x=3 z=9$$