Solve {l}{x+y+2=26}{2x+y-z=24}{x-y+2z=26}

$$\left. \begin{array} { l } { x + y + 2 = 26 } \\ { 2 x + y - z = 24 } \\ { x - y + 2 z = 26 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{25}{2} = 12\frac{1}{2} = 12.5$$

$$y = \frac{23}{2} = 11\frac{1}{2} = 11.5$$

$$z = \frac{25}{2} = 12\frac{1}{2} = 12.5$$

Short Steps Using Substitution

Solve x+y+2=26 for x.

$$x=-y+24$$

Substitute -y+24 for x in the second and third equation.

$$2\left(-y+24\right)+y-z=24 -y+24-y+2z=26$$

Solve these equations for y and z respectively.

$$y=24-z z=1+y$$

Substitute 24-z for y in the equation z=1+y.

$$z=1+24-z$$

Solve z=1+24-z for z.

$$z=\frac{25}{2}$$

Substitute \frac{25}{2} for z in the equation y=24-z.

$$y=24-\frac{25}{2}$$

Calculate y from y=24-\frac{25}{2}.

$$y=\frac{23}{2}$$

Substitute \frac{23}{2} for y in the equation x=-y+24.

$$x=-\frac{23}{2}+24$$

Calculate x from x=-\frac{23}{2}+24.

$$x=\frac{25}{2}$$

The system is now solved.

$$x=\frac{25}{2} y=\frac{23}{2} z=\frac{25}{2}$$