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

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

Datrys ar gyfer x, y, z

$$x=\frac{63}{125}=0.504$$

$$y=-\frac{11}{125}=-0.088$$

$$z=\frac{16}{125}=0.128$$

Camau Byr wrth Ddefnyddio Amnewid

Newid trefn yr hafaliadau.

$$4x-y+7z=3 5x+3y-2z=2 2x+3y+2z=1$$

Datrys 4x-y+7z=3 ar gyfer y.

$$y=4x+7z-3$$

Amnewid 4x+7z-3 am y yn yr ail a'r trydydd hafaliad.

$$5x+3\left(4x+7z-3\right)-2z=2 2x+3\left(4x+7z-3\right)+2z=1$$

Datrys yr hafaliadau hyn ar gyfer x a z yn eu tro.

$$x=-\frac{19}{17}z+\frac{11}{17} z=\frac{10}{23}-\frac{14}{23}x$$

Amnewid -\frac{19}{17}z+\frac{11}{17} am x yn yr hafaliad z=\frac{10}{23}-\frac{14}{23}x.

$$z=\frac{10}{23}-\frac{14}{23}\left(-\frac{19}{17}z+\frac{11}{17}\right)$$

Datrys z=\frac{10}{23}-\frac{14}{23}\left(-\frac{19}{17}z+\frac{11}{17}\right) ar gyfer z.

$$z=\frac{16}{125}$$

Amnewid \frac{16}{125} am z yn yr hafaliad x=-\frac{19}{17}z+\frac{11}{17}.

$$x=-\frac{19}{17}\times \frac{16}{125}+\frac{11}{17}$$

Cyfrifo x o x=-\frac{19}{17}\times \frac{16}{125}+\frac{11}{17}.

$$x=\frac{63}{125}$$

Amnewid \frac{63}{125} am x a \frac{16}{125} am z yn yr hafaliad y=4x+7z-3.

$$y=4\times \frac{63}{125}+7\times \frac{16}{125}-3$$

Cyfrifo y o y=4\times \frac{63}{125}+7\times \frac{16}{125}-3.

$$y=-\frac{11}{125}$$

Mae’r system wedi’i datrys nawr.

$$x=\frac{63}{125} y=-\frac{11}{125} z=\frac{16}{125}$$