Datrys {l}{3x+4y+8z=1}{2z+3y+x=2}{z+2z+2y=3}

$$\left. \begin{array} { l } { 3 x + 4 y + 8 z = 1 } \\ { 2 z + 3 y + x = 2 } \\ { z + 2 z + 2 y = 3 } \end{array} \right.$$

Datrys ar gyfer x, y, z

$$x = -\frac{35}{19} = -1\frac{16}{19} \approx -1.842105263$$

$$y = \frac{21}{19} = 1\frac{2}{19} \approx 1.105263158$$

$$z=\frac{5}{19}\approx 0.263157895$$

Camau Byr wrth Ddefnyddio Amnewid

Newid trefn yr hafaliadau.

$$2z+3y+x=2 3x+4y+8z=1 z+2z+2y=3$$

Datrys 2z+3y+x=2 ar gyfer x.

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

Amnewid -2z-3y+2 am x yn yr hafaliad 3x+4y+8z=1.

$$3\left(-2z-3y+2\right)+4y+8z=1$$

Datrys yr ail hafaliad ar gyfer y a'r trydydd hafaliad ar gyfer z.

$$y=\frac{2}{5}z+1 z=-\frac{2}{3}y+1$$

Amnewid \frac{2}{5}z+1 am y yn yr hafaliad z=-\frac{2}{3}y+1.

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

Datrys z=-\frac{2}{3}\left(\frac{2}{5}z+1\right)+1 ar gyfer z.

$$z=\frac{5}{19}$$

Amnewid \frac{5}{19} am z yn yr hafaliad y=\frac{2}{5}z+1.

$$y=\frac{2}{5}\times \frac{5}{19}+1$$

Cyfrifo y o y=\frac{2}{5}\times \frac{5}{19}+1.

$$y=\frac{21}{19}$$

Amnewid \frac{21}{19} am y a \frac{5}{19} am z yn yr hafaliad x=-2z-3y+2.

$$x=-2\times \frac{5}{19}-3\times \frac{21}{19}+2$$

Cyfrifo x o x=-2\times \frac{5}{19}-3\times \frac{21}{19}+2.

$$x=-\frac{35}{19}$$

Mae’r system wedi’i datrys nawr.

$$x=-\frac{35}{19} y=\frac{21}{19} z=\frac{5}{19}$$