Solve {l}{x+y+z=10}{2*z=10+2y}{2(x+y)+1=z}

$$\left. \begin{array} { l } { x + y + z = 10 } \\ { 2 \times z = 10 + 2 y } \\ { 2 ( x + y ) + 1 = z } \end{array} \right.$$

Solve for x, y, z

$$x=1$$

$$y=2$$

$$z=7$$

Short Steps Using Substitution

Reorder the equations.

$$2\left(x+y\right)+1=z 2z=10+2y x+y+z=10$$

Solve 2\left(x+y\right)+1=z for z.

$$z=2x+2y+1$$

Substitute 2x+2y+1 for z in the second and third equation.

$$2\left(2x+2y+1\right)=10+2y x+y+2x+2y+1=10$$

Solve these equations for y and x respectively.

$$y=4-2x x=3-y$$

Substitute 4-2x for y in the equation x=3-y.

$$x=3-\left(4-2x\right)$$

Solve x=3-\left(4-2x\right) for x.

$$x=1$$

Substitute 1 for x in the equation y=4-2x.

$$y=4-2$$

Calculate y from y=4-2.

$$y=2$$

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

$$z=2\times 1+2\times 2+1$$

Calculate z from z=2\times 1+2\times 2+1.

$$z=7$$

The system is now solved.

$$x=1 y=2 z=7$$