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

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

Solve for x, z, y

$$x=2$$

$$y=6$$

$$z=-2$$

Solution Steps

Consider the first equation. Combine x and x to get 2x.

$$2x+z=2$$

Consider the second equation. Combine x and -x to get 0.

$$z=-2$$

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

$$x-\left(-2\right)=y-2$$

Multiply -1 and -2 to get 2.

$$x+2=y-2$$

Subtract y from both sides.

$$x+2-y=-2$$

Subtract 2 from both sides.

$$x-y=-2-2$$

Subtract 2 from -2 to get -4.

$$x-y=-4$$

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

$$2x-2=2$$

Add 2 to both sides.

$$2x=2+2$$

Add 2 and 2 to get 4.

$$2x=4$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x=2$$

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

$$2-y=-4$$

Subtract 2 from both sides.

$$-y=-4-2$$

Subtract 2 from -4 to get -6.

$$-y=-6$$

Divide both sides by -1.

$$y=\frac{-6}{-1}$$

Fraction \frac{-6}{-1} can be simplified to 6 by removing the negative sign from both the numerator and the denominator.

$$y=6$$

The system is now solved.

$$x=2 z=-2 y=6$$