Solve {l}{x+y=2}{2z-z=1}{2y-3z=-1}

$$\left. \begin{array} { l } { x + y = 2 } \\ { 2 z - z = 1 } \\ { 2 y - 3 z = - 1 } \end{array} \right.$$

Solve for x, y, z

$$x=1$$

$$y=1$$

$$z=1$$

Solution Steps

Consider the second equation. Combine 2z and -z to get z.

$$z=1$$

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

$$2y-3=-1$$

Add 3 to both sides.

$$2y=-1+3$$

Add -1 and 3 to get 2.

$$2y=2$$

Divide both sides by 2.

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

Divide 2 by 2 to get 1.

$$y=1$$

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

$$x+1=2$$

Subtract 1 from both sides.

$$x=2-1$$

Subtract 1 from 2 to get 1.

$$x=1$$

The system is now solved.

$$x=1 y=1 z=1$$