Solve {l}{x-2=4y-2}{42/2+x=y}{3z+y=2x}

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

Solve for x, y, z

$$x = -\frac{20}{3} = -6\frac{2}{3} \approx -6.666666667$$

$$y = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

$$z = -\frac{35}{9} = -3\frac{8}{9} \approx -3.888888889$$

Short Steps Using Substitution

Multiply each equation by the least common multiple of denominators in it. Simplify.

$$x-2=4y-2 10+2x=2y 3z+y=2x$$

Solve x-2=4y-2 for x.

$$x=4y$$

Substitute 4y for x in the second and third equation.

$$10+2\times 4y=2y 3z+y=2\times 4y$$

Solve these equations for y and z respectively.

$$y=-\frac{5}{3} z=\frac{7}{3}y$$

Substitute -\frac{5}{3} for y in the equation z=\frac{7}{3}y.

$$z=\frac{7}{3}\left(-\frac{5}{3}\right)$$

Calculate z from z=\frac{7}{3}\left(-\frac{5}{3}\right).

$$z=-\frac{35}{9}$$

Substitute -\frac{5}{3} for y in the equation x=4y.

$$x=4\left(-\frac{5}{3}\right)$$

Calculate x from x=4\left(-\frac{5}{3}\right).

$$x=-\frac{20}{3}$$

The system is now solved.

$$x=-\frac{20}{3} y=-\frac{5}{3} z=-\frac{35}{9}$$