Solve {l}{x-2y+3z=4}{2x+y+z=3}{5y-7z=-11}

$$\left. \begin{array}{l}{ x - 2 y + 3 z = 4 }\\{ 2 x + y + z = 3 }\\{ 5 y - 7 z = - 11 }\end{array} \right.$$

Solve for x, y, z

$$x=-1$$

$$y=2$$

$$z=3$$

Short Steps Using Substitution

Solve x-2y+3z=4 for x.

$$x=2y-3z+4$$

Substitute 2y-3z+4 for x in the equation 2x+y+z=3.

$$2\left(2y-3z+4\right)+y+z=3$$

Solve the second equation for y and the third equation for z.

$$y=-1+z z=\frac{5}{7}y+\frac{11}{7}$$

Substitute -1+z for y in the equation z=\frac{5}{7}y+\frac{11}{7}.

$$z=\frac{5}{7}\left(-1+z\right)+\frac{11}{7}$$

Solve z=\frac{5}{7}\left(-1+z\right)+\frac{11}{7} for z.

$$z=3$$

Substitute 3 for z in the equation y=-1+z.

$$y=-1+3$$

Calculate y from y=-1+3.

$$y=2$$

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

$$x=2\times 2-3\times 3+4$$

Calculate x from x=2\times 2-3\times 3+4.

$$x=-1$$

The system is now solved.

$$x=-1 y=2 z=3$$