Solve {l}{2x-5y=4}{3y+2z=-3}{7x-3z=1}

$$\left. \begin{array} { l } { 2 x - 5 y = 4 } \\ { 3 y + 2 z = - 3 } \\ { 7 x - 3 z = 1 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{1}{88}\approx 0.011363636$$

$$y=-\frac{35}{44}\approx -0.795454545$$

$$z=-\frac{27}{88}\approx -0.306818182$$

Short Steps Using Substitution

Solve 2x-5y=4 for x.

$$x=\frac{5}{2}y+2$$

Substitute \frac{5}{2}y+2 for x in the equation 7x-3z=1.

$$7\left(\frac{5}{2}y+2\right)-3z=1$$

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

$$y=-\frac{2}{3}z-1 z=\frac{13}{3}+\frac{35}{6}y$$

Substitute -\frac{2}{3}z-1 for y in the equation z=\frac{13}{3}+\frac{35}{6}y.

$$z=\frac{13}{3}+\frac{35}{6}\left(-\frac{2}{3}z-1\right)$$

Solve z=\frac{13}{3}+\frac{35}{6}\left(-\frac{2}{3}z-1\right) for z.

$$z=-\frac{27}{88}$$

Substitute -\frac{27}{88} for z in the equation y=-\frac{2}{3}z-1.

$$y=-\frac{2}{3}\left(-\frac{27}{88}\right)-1$$

Calculate y from y=-\frac{2}{3}\left(-\frac{27}{88}\right)-1.

$$y=-\frac{35}{44}$$

Substitute -\frac{35}{44} for y in the equation x=\frac{5}{2}y+2.

$$x=\frac{5}{2}\left(-\frac{35}{44}\right)+2$$

Calculate x from x=\frac{5}{2}\left(-\frac{35}{44}\right)+2.

$$x=\frac{1}{88}$$

The system is now solved.

$$x=\frac{1}{88} y=-\frac{35}{44} z=-\frac{27}{88}$$