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

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

Solve for x, y, z

$$x=-1$$

$$y=2$$

$$z=1$$

Short Steps Using Substitution

Solve x+y+z=2 for x.

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

Substitute -y-z+2 for x in the equation 2x-y+3z=-1.

$$2\left(-y-z+2\right)-y+3z=-1$$

Solve the second equation for y and the third equation for z.

$$y=2 z=3y-5$$

Substitute 2 for y in the equation z=3y-5.

$$z=3\times 2-5$$

Calculate z from z=3\times 2-5.

$$z=1$$

Substitute 2 for y and 1 for z in the equation x=-y-z+2.

$$x=-2-1+2$$

Calculate x from x=-2-1+2.

$$x=-1$$

The system is now solved.

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