Solve {l}{3(2x+y)+5z=-1}{2(x-3y+4z)=-9}{4(1+x)=-3(z-3y)}

$$\left. \begin{array}{l}{ 3 ( 2 x + y ) + 5 z = - 1 }\\{ 2 ( x - 3 y + 4 z ) = - 9 }\\{ 4 ( 1 + x ) = - 3 ( z - 3 y ) }\end{array} \right.$$

Solve for x, y, z

$$x=\frac{1}{2}=0.5$$

$$y=\frac{1}{3}\approx 0.333333333$$

$$z=-1$$

Short Steps Using Substitution

Solve 3\left(2x+y\right)+5z=-1 for x.

$$x=-\frac{1}{2}y-\frac{5}{6}z-\frac{1}{6}$$

Substitute -\frac{1}{2}y-\frac{5}{6}z-\frac{1}{6} for x in the second and third equation.

$$2\left(-\frac{1}{2}y-\frac{5}{6}z-\frac{1}{6}-3y+4z\right)=-9 4\left(1-\frac{1}{2}y-\frac{5}{6}z-\frac{1}{6}\right)=-3\left(z-3y\right)$$

Solve these equations for y and z respectively.

$$y=\frac{26}{21}+\frac{19}{21}z z=10-33y$$

Substitute \frac{26}{21}+\frac{19}{21}z for y in the equation z=10-33y.

$$z=10-33\left(\frac{26}{21}+\frac{19}{21}z\right)$$

Solve z=10-33\left(\frac{26}{21}+\frac{19}{21}z\right) for z.

$$z=-1$$

Substitute -1 for z in the equation y=\frac{26}{21}+\frac{19}{21}z.

$$y=\frac{26}{21}+\frac{19}{21}\left(-1\right)$$

Calculate y from y=\frac{26}{21}+\frac{19}{21}\left(-1\right).

$$y=\frac{1}{3}$$

Substitute \frac{1}{3} for y and -1 for z in the equation x=-\frac{1}{2}y-\frac{5}{6}z-\frac{1}{6}.

$$x=-\frac{1}{2}\times \frac{1}{3}-\frac{5}{6}\left(-1\right)-\frac{1}{6}$$

Calculate x from x=-\frac{1}{2}\times \frac{1}{3}-\frac{5}{6}\left(-1\right)-\frac{1}{6}.

$$x=\frac{1}{2}$$

The system is now solved.

$$x=\frac{1}{2} y=\frac{1}{3} z=-1$$