Solve {l}{100x+100y+10z=100}{x+y=6}{x+z=1000}

$$\left. \begin{array} { l } { 100 x + 100 y + 10 z = 100 } \\ { x + y = 6 } \\ { x + z = 1000 } \end{array} \right.$$

Solve for x, y, z

$$x=1050$$

$$y=-1044$$

$$z=-50$$

Short Steps Using Substitution

Reorder the equations.

$$x+y=6 100x+100y+10z=100 x+z=1000$$

Solve x+y=6 for x.

$$x=-y+6$$

Substitute -y+6 for x in the second and third equation.

$$100\left(-y+6\right)+100y+10z=100 -y+6+z=1000$$

Solve these equations for z and y respectively.

$$z=-50 y=-994+z$$

Substitute -50 for z in the equation y=-994+z.

$$y=-994-50$$

Calculate y from y=-994-50.

$$y=-1044$$

Substitute -1044 for y in the equation x=-y+6.

$$x=-\left(-1044\right)+6$$

Calculate x from x=-\left(-1044\right)+6.

$$x=1050$$

The system is now solved.

$$x=1050 y=-1044 z=-50$$