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

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

Solve for x, y, z

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

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

$$z=2$$

Short Steps Using Substitution

Solve x-y=1 for x.

$$x=y+1$$

Substitute y+1 for x in the second and third equation.

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

Solve these equations for y and z respectively.

$$y=-\frac{3}{4}+\frac{5}{8}z z=2y+1$$

Substitute -\frac{3}{4}+\frac{5}{8}z for y in the equation z=2y+1.

$$z=2\left(-\frac{3}{4}+\frac{5}{8}z\right)+1$$

Solve z=2\left(-\frac{3}{4}+\frac{5}{8}z\right)+1 for z.

$$z=2$$

Substitute 2 for z in the equation y=-\frac{3}{4}+\frac{5}{8}z.

$$y=-\frac{3}{4}+\frac{5}{8}\times 2$$

Calculate y from y=-\frac{3}{4}+\frac{5}{8}\times 2.

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

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

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

Calculate x from x=\frac{1}{2}+1.

$$x=\frac{3}{2}$$

The system is now solved.

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