Solve {l}{y=2z-1}{x+y+z=44}{3x+4y+6z=171}

$$\left. \begin{array} { l } { y = 2 z - 1 } \\ { x + y + z = 44 } \\ { 3 x + 4 y + 6 z = 171 } \end{array} \right.$$

Solve for y, z, x

$$x=21$$

$$y=15$$

$$z=8$$

Short Steps Using Substitution

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

$$x+2z-1+z=44 3x+4\left(2z-1\right)+6z=171$$

Solve these equations for z and x respectively.

$$z=-\frac{1}{3}x+15 x=\frac{175}{3}-\frac{14}{3}z$$

Substitute -\frac{1}{3}x+15 for z in the equation x=\frac{175}{3}-\frac{14}{3}z.

$$x=\frac{175}{3}-\frac{14}{3}\left(-\frac{1}{3}x+15\right)$$

Solve x=\frac{175}{3}-\frac{14}{3}\left(-\frac{1}{3}x+15\right) for x.

$$x=21$$

Substitute 21 for x in the equation z=-\frac{1}{3}x+15.

$$z=-\frac{1}{3}\times 21+15$$

Calculate z from z=-\frac{1}{3}\times 21+15.

$$z=8$$

Substitute 8 for z in the equation y=2z-1.

$$y=2\times 8-1$$

Calculate y from y=2\times 8-1.

$$y=15$$

The system is now solved.

$$y=15 z=8 x=21$$