Solve {l}{x-y+z=5}{-x+2y=-6}{3x=6}

$$\left\{ \begin{array} { l } { x - y + z = 5 } \\ { - x + 2 y = - 6 } \\ { 3 x = 6 } \end{array} \right.$$

Solve for x, y, z

$$x=2$$

$$y=-2$$

$$z=1$$

Solution Steps

Consider the third equation. Divide both sides by 3.

$$x=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$x=2$$

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

$$-2+2y=-6$$

Add 2 to both sides.

$$2y=-6+2$$

Add -6 and 2 to get -4.

$$2y=-4$$

Divide both sides by 2.

$$y=\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$y=-2$$

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

$$2-\left(-2\right)+z=5$$

Multiply -1 and -2 to get 2.

$$2+2+z=5$$

Add 2 and 2 to get 4.

$$4+z=5$$

Subtract 4 from both sides.

$$z=5-4$$

Subtract 4 from 5 to get 1.

$$z=1$$

The system is now solved.

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