Solve {l}{3x+3y-z=4}{4x-3y+z=2}{x-y+z=1}

$$\left. \begin{array} { l } { 3 x + 3 y - z = 4 } \\ { 4 x - 3 y + z = 2 } \\ { x - y + z = 1 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{6}{7}\approx 0.857142857$$

$$y=\frac{11}{14}\approx 0.785714286$$

$$z=\frac{13}{14}\approx 0.928571429$$

Short Steps Using Substitution

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

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

Substitute 3x+3y-4 for z in the second and third equation.

$$4x-3y+3x+3y-4=2 x-y+3x+3y-4=1$$

Solve these equations for x and y respectively.

$$x=\frac{6}{7} y=-2x+\frac{5}{2}$$

Substitute \frac{6}{7} for x in the equation y=-2x+\frac{5}{2}.

$$y=-2\times \frac{6}{7}+\frac{5}{2}$$

Calculate y from y=-2\times \frac{6}{7}+\frac{5}{2}.

$$y=\frac{11}{14}$$

Substitute \frac{6}{7} for x and \frac{11}{14} for y in the equation z=3x+3y-4.

$$z=3\times \frac{6}{7}+3\times \frac{11}{14}-4$$

Calculate z from z=3\times \frac{6}{7}+3\times \frac{11}{14}-4.

$$z=\frac{13}{14}$$

The system is now solved.

$$x=\frac{6}{7} y=\frac{11}{14} z=\frac{13}{14}$$