Solve {l}{2x+6y-5z=-4}{x+y-z=0}{z=-1}-0

$$\left.\begin{array} { l } { 2 x + 6 y - 5 z = - 4 } \\ { x + y - z = 0 } \\ { z = - 1 } \end{array} \right\} - 0$$

Solve for x, y, z

$$x=\frac{3}{4}=0.75$$

$$y = -\frac{7}{4} = -1\frac{3}{4} = -1.75$$

$$z=-1$$

Short Steps Using Substitution

Reorder the equations.

$$z=-1 x+y-z=0 2x+6y-5z=-4$$

Substitute -1 for z in the second and third equation.

$$x+y-\left(-1\right)=0 2x+6y-5\left(-1\right)=-4$$

Solve these equations for y and x respectively.

$$y=-x-1 x=-\frac{9}{2}-3y$$

Substitute -x-1 for y in the equation x=-\frac{9}{2}-3y.

$$x=-\frac{9}{2}-3\left(-x-1\right)$$

Solve x=-\frac{9}{2}-3\left(-x-1\right) for x.

$$x=\frac{3}{4}$$

Substitute \frac{3}{4} for x in the equation y=-x-1.

$$y=-\frac{3}{4}-1$$

Calculate y from y=-\frac{3}{4}-1.

$$y=-\frac{7}{4}$$

The system is now solved.

$$x=\frac{3}{4} y=-\frac{7}{4} z=-1$$