Solve {l}{2x+y=3}{2x+9z=4}{3z+5y=8}

$$\left. \begin{array} { l } { 2 x + y = 3 } \\ { 2 x + 9 z = 4 } \\ { 3 z + 5 y = 8 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{25}{32}=0.78125$$

$$y = \frac{23}{16} = 1\frac{7}{16} = 1.4375$$

$$z=\frac{13}{48}\approx 0.270833333$$

Short Steps Using Substitution

Solve 2x+y=3 for y.

$$y=-2x+3$$

Substitute -2x+3 for y in the equation 3z+5y=8.

$$3z+5\left(-2x+3\right)=8$$

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

$$x=-\frac{9}{2}z+2 z=\frac{10}{3}x-\frac{7}{3}$$

Substitute -\frac{9}{2}z+2 for x in the equation z=\frac{10}{3}x-\frac{7}{3}.

$$z=\frac{10}{3}\left(-\frac{9}{2}z+2\right)-\frac{7}{3}$$

Solve z=\frac{10}{3}\left(-\frac{9}{2}z+2\right)-\frac{7}{3} for z.

$$z=\frac{13}{48}$$

Substitute \frac{13}{48} for z in the equation x=-\frac{9}{2}z+2.

$$x=-\frac{9}{2}\times \frac{13}{48}+2$$

Calculate x from x=-\frac{9}{2}\times \frac{13}{48}+2.

$$x=\frac{25}{32}$$

Substitute \frac{25}{32} for x in the equation y=-2x+3.

$$y=-2\times \frac{25}{32}+3$$

Calculate y from y=-2\times \frac{25}{32}+3.

$$y=\frac{23}{16}$$

The system is now solved.

$$x=\frac{25}{32} y=\frac{23}{16} z=\frac{13}{48}$$