Solve {l}{4x+y+z=3}{3x-y-z=7}{-x+2y+3z=-1}

$$\left. \begin{array} { l } { 4 x + y + z = 3 } \\ { 3 x - y - z = 7 } \\ { - x + 2 y + 3 z = - 1 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$$

$$y = -\frac{60}{7} = -8\frac{4}{7} \approx -8.571428571$$

$$z = \frac{41}{7} = 5\frac{6}{7} \approx 5.857142857$$

Short Steps Using Substitution

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

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

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

$$3x-\left(-4x-z+3\right)-z=7 -x+2\left(-4x-z+3\right)+3z=-1$$

Solve these equations for x and z respectively.

$$x=\frac{10}{7} z=9x-7$$

Substitute \frac{10}{7} for x in the equation z=9x-7.

$$z=9\times \frac{10}{7}-7$$

Calculate z from z=9\times \frac{10}{7}-7.

$$z=\frac{41}{7}$$

Substitute \frac{10}{7} for x and \frac{41}{7} for z in the equation y=-4x-z+3.

$$y=-4\times \frac{10}{7}-\frac{41}{7}+3$$

Calculate y from y=-4\times \frac{10}{7}-\frac{41}{7}+3.

$$y=-\frac{60}{7}$$

The system is now solved.

$$x=\frac{10}{7} y=-\frac{60}{7} z=\frac{41}{7}$$