Solve {l}{x+y+z=44}{x+50y+200z=4}{x+y+2z=58}

$$\left. \begin{array} { l } { x + y + z = 44 } \\ { x + 50 y + 200 z = 4 } \\ { x + y + 2 z = 58 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{4296}{49} = 87\frac{33}{49} \approx 87.673469388$$

$$y = -\frac{2826}{49} = -57\frac{33}{49} \approx -57.673469388$$

$$z=14$$

Short Steps Using Substitution

Solve x+y+z=44 for x.

$$x=-y-z+44$$

Substitute -y-z+44 for x in the second and third equation.

$$-y-z+44+50y+200z=4 -y-z+44+y+2z=58$$

Solve these equations for y and z respectively.

$$y=-\frac{199}{49}z-\frac{40}{49} z=14$$

Substitute 14 for z in the equation y=-\frac{199}{49}z-\frac{40}{49}.

$$y=-\frac{199}{49}\times 14-\frac{40}{49}$$

Calculate y from y=-\frac{199}{49}\times 14-\frac{40}{49}.

$$y=-\frac{2826}{49}$$

Substitute -\frac{2826}{49} for y and 14 for z in the equation x=-y-z+44.

$$x=-\left(-\frac{2826}{49}\right)-14+44$$

Calculate x from x=-\left(-\frac{2826}{49}\right)-14+44.

$$x=\frac{4296}{49}$$

The system is now solved.

$$x=\frac{4296}{49} y=-\frac{2826}{49} z=14$$