Solve {l}{3x+4y-z=1}{5z-9y=5}{9y-x+8z=1}

$$\left. \begin{array} { l } { 3 x + 4 y - z = 1 } \\ { 5 z - 9 y = 5 } \\ { 9 y - x + 8 z = 1 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{311}{362}\approx 0.859116022$$

$$y=-\frac{95}{362}\approx -0.262430939$$

$$z=\frac{191}{362}\approx 0.527624309$$

Short Steps Using Substitution

Solve 3x+4y-z=1 for z.

$$z=3x+4y-1$$

Substitute 3x+4y-1 for z in the second and third equation.

$$5\left(3x+4y-1\right)-9y=5 9y-x+8\left(3x+4y-1\right)=1$$

Solve these equations for y and x respectively.

$$y=\frac{10}{11}-\frac{15}{11}x x=-\frac{41}{23}y+\frac{9}{23}$$

Substitute \frac{10}{11}-\frac{15}{11}x for y in the equation x=-\frac{41}{23}y+\frac{9}{23}.

$$x=-\frac{41}{23}\left(\frac{10}{11}-\frac{15}{11}x\right)+\frac{9}{23}$$

Solve x=-\frac{41}{23}\left(\frac{10}{11}-\frac{15}{11}x\right)+\frac{9}{23} for x.

$$x=\frac{311}{362}$$

Substitute \frac{311}{362} for x in the equation y=\frac{10}{11}-\frac{15}{11}x.

$$y=\frac{10}{11}-\frac{15}{11}\times \frac{311}{362}$$

Calculate y from y=\frac{10}{11}-\frac{15}{11}\times \frac{311}{362}.

$$y=-\frac{95}{362}$$

Substitute -\frac{95}{362} for y and \frac{311}{362} for x in the equation z=3x+4y-1.

$$z=3\times \frac{311}{362}+4\left(-\frac{95}{362}\right)-1$$

Calculate z from z=3\times \frac{311}{362}+4\left(-\frac{95}{362}\right)-1.

$$z=\frac{191}{362}$$

The system is now solved.

$$x=\frac{311}{362} y=-\frac{95}{362} z=\frac{191}{362}$$