Solve {l}{x-2y=-4}{y-z=3}{2z+x=47}

$$\left\{ \begin{array} { l } { x - 2 y = - 4 } \\ { y - z = 3 } \\ { 2 z + x = 47 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{49}{2} = 24\frac{1}{2} = 24.5$$

$$y = \frac{57}{4} = 14\frac{1}{4} = 14.25$$

$$z = \frac{45}{4} = 11\frac{1}{4} = 11.25$$

Short Steps Using Substitution

Solve x-2y=-4 for x.

$$x=-4+2y$$

Substitute -4+2y for x in the equation 2z+x=47.

$$2z-4+2y=47$$

Solve the second equation for y and the third equation for z.

$$y=z+3 z=\frac{51}{2}-y$$

Substitute z+3 for y in the equation z=\frac{51}{2}-y.

$$z=\frac{51}{2}-\left(z+3\right)$$

Solve z=\frac{51}{2}-\left(z+3\right) for z.

$$z=\frac{45}{4}$$

Substitute \frac{45}{4} for z in the equation y=z+3.

$$y=\frac{45}{4}+3$$

Calculate y from y=\frac{45}{4}+3.

$$y=\frac{57}{4}$$

Substitute \frac{57}{4} for y in the equation x=-4+2y.

$$x=-4+2\times \frac{57}{4}$$

Calculate x from x=-4+2\times \frac{57}{4}.

$$x=\frac{49}{2}$$

The system is now solved.

$$x=\frac{49}{2} y=\frac{57}{4} z=\frac{45}{4}$$