Solve {l}{3x+2z=0}{5x+2y=28}{-y+4z=-63}

$$\left. \begin{array} { l } { 3 x + 2 z = 0 } \\ { 5 x + 2 y = 28 } \\ { - y + 4 z = - 63 } \end{array} \right.$$

Solve for x, z, y

$$x=14$$

$$y=-21$$

$$z=-21$$

Short Steps Using Substitution

Reorder the equations.

$$-y+4z=-63 5x+2y=28 3x+2z=0$$

Solve -y+4z=-63 for y.

$$y=4z+63$$

Substitute 4z+63 for y in the equation 5x+2y=28.

$$5x+2\left(4z+63\right)=28$$

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

$$z=-\frac{49}{4}-\frac{5}{8}x x=-\frac{2}{3}z$$

Substitute -\frac{49}{4}-\frac{5}{8}x for z in the equation x=-\frac{2}{3}z.

$$x=-\frac{2}{3}\left(-\frac{49}{4}-\frac{5}{8}x\right)$$

Solve x=-\frac{2}{3}\left(-\frac{49}{4}-\frac{5}{8}x\right) for x.

$$x=14$$

Substitute 14 for x in the equation z=-\frac{49}{4}-\frac{5}{8}x.

$$z=-\frac{49}{4}-\frac{5}{8}\times 14$$

Calculate z from z=-\frac{49}{4}-\frac{5}{8}\times 14.

$$z=-21$$

Substitute -21 for z in the equation y=4z+63.

$$y=4\left(-21\right)+63$$

Calculate y from y=4\left(-21\right)+63.

$$y=-21$$

The system is now solved.

$$x=14 z=-21 y=-21$$