Solve {l}{3x+2y+z=1}{4x+y+7=0}{x+3y+7=2}

$$\left. \begin{array} { l } { 3 x + 2 y + z = 1 } \\ { 4 x + y + 7 = 0 } \\ { x + 3 y + 7 = 2 } \end{array} \right.$$

Solve for x, y, z

$$x = -\frac{16}{11} = -1\frac{5}{11} \approx -1.454545455$$

$$y = -\frac{13}{11} = -1\frac{2}{11} \approx -1.181818182$$

$$z = \frac{85}{11} = 7\frac{8}{11} \approx 7.727272727$$

Short Steps Using Substitution

Solve 3x+2y+z=1 for z.

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

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

$$y=-4x-7 x=-3y-5$$

Substitute -4x-7 for y in the equation x=-3y-5.

$$x=-3\left(-4x-7\right)-5$$

Solve x=-3\left(-4x-7\right)-5 for x.

$$x=-\frac{16}{11}$$

Substitute -\frac{16}{11} for x in the equation y=-4x-7.

$$y=-4\left(-\frac{16}{11}\right)-7$$

Calculate y from y=-4\left(-\frac{16}{11}\right)-7.

$$y=-\frac{13}{11}$$

Substitute -\frac{13}{11} for y and -\frac{16}{11} for x in the equation z=-3x-2y+1.

$$z=-3\left(-\frac{16}{11}\right)-2\left(-\frac{13}{11}\right)+1$$

Calculate z from z=-3\left(-\frac{16}{11}\right)-2\left(-\frac{13}{11}\right)+1.

$$z=\frac{85}{11}$$

The system is now solved.

$$x=-\frac{16}{11} y=-\frac{13}{11} z=\frac{85}{11}$$