Datrys {l}{1/10U_{1}+(U_{1}-U_{2})1/2=5I_{x}+2}{1/2(U_{1}-U_{2})+5I_{x}+1/4U_{2}=0}{I_{x}=frac{6}{13}}

$$\left. \begin{array} { l } { \frac { 1 } { 10 } U _ { 1 } + ( U _ { 1 } - U _ { 2 } ) \frac { 1 } { 2 } = 5 I _ { x } + 2 } \\ { \frac { 1 } { 2 } ( U _ { 1 } - U _ { 2 } ) + 5 I _ { x } + \frac { 1 } { 4 } U _ { 2 } = 0 } \\ { I _ { x } = \frac { 6 } { 13 } } \end{array} \right.$$

Datrys ar gyfer U_1, U_2, I_x

$$U_{1} = -\frac{290}{13} = -22\frac{4}{13} \approx -22.307692308$$

$$U_{2} = -\frac{460}{13} = -35\frac{5}{13} \approx -35.384615385$$

$$I_{x}=\frac{6}{13}\approx 0.461538462$$

Camau Byr wrth Ddefnyddio Amnewid

Newid trefn yr hafaliadau.

$$I_{x}=\frac{6}{13} \frac{1}{2}\left(U_{1}-U_{2}\right)+5I_{x}+\frac{1}{4}U_{2}=0 \frac{1}{10}U_{1}+\left(U_{1}-U_{2}\right)\times \frac{1}{2}=5I_{x}+2$$

Amnewid \frac{6}{13} am I_{x} yn yr ail a'r trydydd hafaliad.

$$\frac{1}{2}\left(U_{1}-U_{2}\right)+5\times \frac{6}{13}+\frac{1}{4}U_{2}=0 \frac{1}{10}U_{1}+\left(U_{1}-U_{2}\right)\times \frac{1}{2}=5\times \frac{6}{13}+2$$

Datrys yr hafaliadau hyn ar gyfer U_{2} a U_{1} yn eu tro.

$$U_{2}=\frac{120}{13}+2U_{1} U_{1}=\frac{280}{39}+\frac{5}{6}U_{2}$$

Amnewid \frac{120}{13}+2U_{1} am U_{2} yn yr hafaliad U_{1}=\frac{280}{39}+\frac{5}{6}U_{2}.

$$U_{1}=\frac{280}{39}+\frac{5}{6}\left(\frac{120}{13}+2U_{1}\right)$$

Datrys U_{1}=\frac{280}{39}+\frac{5}{6}\left(\frac{120}{13}+2U_{1}\right) ar gyfer U_{1}.

$$U_{1}=-\frac{290}{13}$$

Amnewid -\frac{290}{13} am U_{1} yn yr hafaliad U_{2}=\frac{120}{13}+2U_{1}.

$$U_{2}=\frac{120}{13}+2\left(-\frac{290}{13}\right)$$

Cyfrifo U_{2} o U_{2}=\frac{120}{13}+2\left(-\frac{290}{13}\right).

$$U_{2}=-\frac{460}{13}$$

Mae’r system wedi’i datrys nawr.

$$U_{1}=-\frac{290}{13} U_{2}=-\frac{460}{13} I_{x}=\frac{6}{13}$$