Solve {l}{x-y=1}{x+y+z=26}{y+z-x=6}

$$\left\{ \begin{array} { l } { x - y = 1 } \\ { x + y + z = 26 } \\ { y + z - x = 6 } \end{array} \right.$$

Solve for x, y, z

$$x=10$$

$$y=9$$

$$z=7$$

Short Steps Using Substitution

Solve x-y=1 for x.

$$x=y+1$$

Substitute y+1 for x in the second and third equation.

$$y+1+y+z=26 y+z-\left(y+1\right)=6$$

Solve these equations for y and z respectively.

$$y=\frac{25}{2}-\frac{1}{2}z z=7$$

Substitute 7 for z in the equation y=\frac{25}{2}-\frac{1}{2}z.

$$y=\frac{25}{2}-\frac{1}{2}\times 7$$

Calculate y from y=\frac{25}{2}-\frac{1}{2}\times 7.

$$y=9$$

Substitute 9 for y in the equation x=y+1.

$$x=9+1$$

Calculate x from x=9+1.

$$x=10$$

The system is now solved.

$$x=10 y=9 z=7$$