Solve {l}{9+16+3x+4y+z=0}{25-5y+z=0}{4+1-2x-y+z=0}

$$\left\{ \begin{array} { l } { 9 + 16 + 3 x + 4 y + z = 0 } \\ { 25 - 5 y + z = 0 } \\ { 4 + 1 - 2 x - y + z = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=-6$$

$$y=2$$

$$z=-15$$

Short Steps Using Substitution

Solve 9+16+3x+4y+z=0 for z.

$$z=-25-3x-4y$$

Substitute -25-3x-4y for z in the second and third equation.

$$25-5y-25-3x-4y=0 4+1-2x-y-25-3x-4y=0$$

Solve these equations for y and x respectively.

$$y=-\frac{1}{3}x x=-4-y$$

Substitute -\frac{1}{3}x for y in the equation x=-4-y.

$$x=-4-\left(-\frac{1}{3}x\right)$$

Solve x=-4-\left(-\frac{1}{3}x\right) for x.

$$x=-6$$

Substitute -6 for x in the equation y=-\frac{1}{3}x.

$$y=-\frac{1}{3}\left(-6\right)$$

Calculate y from y=-\frac{1}{3}\left(-6\right).

$$y=2$$

Substitute 2 for y and -6 for x in the equation z=-25-3x-4y.

$$z=-25-3\left(-6\right)-4\times 2$$

Calculate z from z=-25-3\left(-6\right)-4\times 2.

$$z=-15$$

The system is now solved.

$$x=-6 y=2 z=-15$$