Datrys {l}{10x+10y-20z=60}{15x+20y+20z=-25}{-5x+30y-10z=45}

$$\left\{ \begin{array} { l } { 10 x + 10 y - 20 z = 60 } \\ { 15 x + 20 y + 20 z = - 25 } \\ { - 5 x + 30 y - 10 z = 45 } \end{array} \right.$$

Datrys ar gyfer x, y, z

$$x=\frac{17}{37}\approx 0.459459459$$

$$y=\frac{29}{37}\approx 0.783783784$$

$$z = -\frac{88}{37} = -2\frac{14}{37} \approx -2.378378378$$

Camau Byr wrth Ddefnyddio Amnewid

Datrys 10x+10y-20z=60 ar gyfer x.

$$x=6-y+2z$$

Amnewid 6-y+2z am x yn yr ail a'r trydydd hafaliad.

$$15\left(6-y+2z\right)+20y+20z=-25 -5\left(6-y+2z\right)+30y-10z=45$$

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

$$y=-23-10z z=-\frac{15}{4}+\frac{7}{4}y$$

Amnewid -23-10z am y yn yr hafaliad z=-\frac{15}{4}+\frac{7}{4}y.

$$z=-\frac{15}{4}+\frac{7}{4}\left(-23-10z\right)$$

Datrys z=-\frac{15}{4}+\frac{7}{4}\left(-23-10z\right) ar gyfer z.

$$z=-\frac{88}{37}$$

Amnewid -\frac{88}{37} am z yn yr hafaliad y=-23-10z.

$$y=-23-10\left(-\frac{88}{37}\right)$$

Cyfrifo y o y=-23-10\left(-\frac{88}{37}\right).

$$y=\frac{29}{37}$$

Amnewid \frac{29}{37} am y a -\frac{88}{37} am z yn yr hafaliad x=6-y+2z.

$$x=6-\frac{29}{37}+2\left(-\frac{88}{37}\right)$$

Cyfrifo x o x=6-\frac{29}{37}+2\left(-\frac{88}{37}\right).

$$x=\frac{17}{37}$$

Mae’r system wedi’i datrys nawr.

$$x=\frac{17}{37} y=\frac{29}{37} z=-\frac{88}{37}$$