Solve {l}{2x-3y+z=-1}{6x-9y-4z=4}{4x+6y-z=5}

$$\left. \begin{array} { l } { 2 x - 3 y + z = - 1 } \\ { 6 x - 9 y - 4 z = 4 } \\ { 4 x + 6 y - z = 5 } \end{array} \right.$$

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

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

Substitute -2x+3y-1 for z in the second and third equation.

$$6x-9y-4\left(-2x+3y-1\right)=4 4x+6y-\left(-2x+3y-1\right)=5$$

Solve these equations for y and x respectively.

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

Substitute \frac{2}{3}x for y in the equation x=-\frac{1}{2}y+\frac{2}{3}.

$$x=-\frac{1}{2}\times \frac{2}{3}x+\frac{2}{3}$$

Solve x=-\frac{1}{2}\times \frac{2}{3}x+\frac{2}{3} for x.

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

Substitute \frac{1}{2} for x in the equation y=\frac{2}{3}x.

$$y=\frac{2}{3}\times \frac{1}{2}$$

Calculate y from y=\frac{2}{3}\times \frac{1}{2}.

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

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

$$z=-2\times \frac{1}{2}+3\times \frac{1}{3}-1$$

Calculate z from z=-2\times \frac{1}{2}+3\times \frac{1}{3}-1.

$$z=-1$$

The system is now solved.

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