Solve {l}{x+y-4z=0}{4x+7z=41}{4x+3y=41}

$$\left\{ \begin{array}{l}{ x + y - 4 z = 0 }\\{ 4 x + 7 z = 41 }\\{ 4 x + 3 y = 41 }\end{array} \right.$$

Solve for x, y, z

$$x=5$$

$$y=7$$

$$z=3$$

Short Steps Using Substitution

Solve x+y-4z=0 for x.

$$x=-y+4z$$

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

$$4\left(-y+4z\right)+7z=41 4\left(-y+4z\right)+3y=41$$

Solve these equations for y and z respectively.

$$y=-\frac{41}{4}+\frac{23}{4}z z=\frac{41}{16}+\frac{1}{16}y$$

Substitute -\frac{41}{4}+\frac{23}{4}z for y in the equation z=\frac{41}{16}+\frac{1}{16}y.

$$z=\frac{41}{16}+\frac{1}{16}\left(-\frac{41}{4}+\frac{23}{4}z\right)$$

Solve z=\frac{41}{16}+\frac{1}{16}\left(-\frac{41}{4}+\frac{23}{4}z\right) for z.

$$z=3$$

Substitute 3 for z in the equation y=-\frac{41}{4}+\frac{23}{4}z.

$$y=-\frac{41}{4}+\frac{23}{4}\times 3$$

Calculate y from y=-\frac{41}{4}+\frac{23}{4}\times 3.

$$y=7$$

Substitute 7 for y and 3 for z in the equation x=-y+4z.

$$x=-7+4\times 3$$

Calculate x from x=-7+4\times 3.

$$x=5$$

The system is now solved.

$$x=5 y=7 z=3$$