Solve {l}{2x+y+z=36}{x=y+1}{3x-2y-z=5}

$$\left. \begin{array} { l } { 2 x + y + z = 36 } \\ { x = y + 1 } \\ { 3 x - 2 y - z = 5 } \end{array} \right.$$

Solve for x, y, z

$$x=10$$

$$y=9$$

$$z=7$$

Short Steps Using Substitution

Reorder the equations.

$$x=y+1 2x+y+z=36 3x-2y-z=5$$

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

$$2\left(y+1\right)+y+z=36 3\left(y+1\right)-2y-z=5$$

Solve these equations for y and z respectively.

$$y=\frac{34}{3}-\frac{1}{3}z z=y-2$$

Substitute \frac{34}{3}-\frac{1}{3}z for y in the equation z=y-2.

$$z=\frac{34}{3}-\frac{1}{3}z-2$$

Solve z=\frac{34}{3}-\frac{1}{3}z-2 for z.

$$z=7$$

Substitute 7 for z in the equation y=\frac{34}{3}-\frac{1}{3}z.

$$y=\frac{34}{3}-\frac{1}{3}\times 7$$

Calculate y from y=\frac{34}{3}-\frac{1}{3}\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.

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