Solve {l}{x+y+z=159}{3x+4y+6z=98}{4x-z=12}

$$\left. \begin{array} { l } { x + y + z = 159 } \\ { 3 x + 4 y + 6 z = 98 } \\ { 4 x - z = 12 } \end{array} \right.$$

Solve for x, y, z

$$x = -\frac{514}{7} = -73\frac{3}{7} \approx -73.428571429$$

$$y = \frac{3767}{7} = 538\frac{1}{7} \approx 538.142857143$$

$$z = -\frac{2140}{7} = -305\frac{5}{7} \approx -305.714285714$$

Short Steps Using Substitution

Solve x+y+z=159 for x.

$$x=-y-z+159$$

Substitute -y-z+159 for x in the second and third equation.

$$3\left(-y-z+159\right)+4y+6z=98 4\left(-y-z+159\right)-z=12$$

Solve these equations for y and z respectively.

$$y=-3z-379 z=\frac{624}{5}-\frac{4}{5}y$$

Substitute -3z-379 for y in the equation z=\frac{624}{5}-\frac{4}{5}y.

$$z=\frac{624}{5}-\frac{4}{5}\left(-3z-379\right)$$

Solve z=\frac{624}{5}-\frac{4}{5}\left(-3z-379\right) for z.

$$z=-\frac{2140}{7}$$

Substitute -\frac{2140}{7} for z in the equation y=-3z-379.

$$y=-3\left(-\frac{2140}{7}\right)-379$$

Calculate y from y=-3\left(-\frac{2140}{7}\right)-379.

$$y=\frac{3767}{7}$$

Substitute \frac{3767}{7} for y and -\frac{2140}{7} for z in the equation x=-y-z+159.

$$x=-\frac{3767}{7}-\left(-\frac{2140}{7}\right)+159$$

Calculate x from x=-\frac{3767}{7}-\left(-\frac{2140}{7}\right)+159.

$$x=-\frac{514}{7}$$

The system is now solved.

$$x=-\frac{514}{7} y=\frac{3767}{7} z=-\frac{2140}{7}$$