Solve {l}{x+2y-z=-4}{2y+z=2}{2y=-2}

$$\left. \begin{array} { l } { x + 2 y - z = - 4 } \\ { 2 y + z = 2 } \\ { 2 y = - 2 } \end{array} \right.$$

Solve for x, y, z

$$x=2$$

$$y=-1$$

$$z=4$$

Solution Steps

Consider the third equation. Divide both sides by 2.

$$y=\frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$y=-1$$

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

$$2\left(-1\right)+z=2$$

Multiply 2 and -1 to get -2.

$$-2+z=2$$

Add 2 to both sides.

$$z=2+2$$

Add 2 and 2 to get 4.

$$z=4$$

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

$$x+2\left(-1\right)-4=-4$$

Do the multiplications.

$$x-2-4=-4$$

Subtract 4 from -2 to get -6.

$$x-6=-4$$

Add 6 to both sides.

$$x=-4+6$$

Add -4 and 6 to get 2.

$$x=2$$

The system is now solved.

$$x=2 y=-1 z=4$$