Datrys {r}{2x+y-2z=-1}{3x-3y=5+z}{-2x+x+3z=5}

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

Datrys ar gyfer x, y, z

$$x = \frac{41}{20} = 2\frac{1}{20} = 2.05$$

$$y=-\frac{2}{5}=-0.4$$

$$z = \frac{47}{20} = 2\frac{7}{20} = 2.35$$

Camau Byr wrth Ddefnyddio Amnewid

Datrys 2x+y-2z=-1 ar gyfer y.

$$y=-2x+2z-1$$

Amnewid -2x+2z-1 am y yn yr hafaliad 3x-3y=5+z.

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

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

$$x=\frac{7}{9}z+\frac{2}{9} z=\frac{5}{3}+\frac{1}{3}x$$

Amnewid \frac{7}{9}z+\frac{2}{9} am x yn yr hafaliad z=\frac{5}{3}+\frac{1}{3}x.

$$z=\frac{5}{3}+\frac{1}{3}\left(\frac{7}{9}z+\frac{2}{9}\right)$$

Datrys z=\frac{5}{3}+\frac{1}{3}\left(\frac{7}{9}z+\frac{2}{9}\right) ar gyfer z.

$$z=\frac{47}{20}$$

Amnewid \frac{47}{20} am z yn yr hafaliad x=\frac{7}{9}z+\frac{2}{9}.

$$x=\frac{7}{9}\times \frac{47}{20}+\frac{2}{9}$$

Cyfrifo x o x=\frac{7}{9}\times \frac{47}{20}+\frac{2}{9}.

$$x=\frac{41}{20}$$

Amnewid \frac{41}{20} am x a \frac{47}{20} am z yn yr hafaliad y=-2x+2z-1.

$$y=-2\times \frac{41}{20}+2\times \frac{47}{20}-1$$

Cyfrifo y o y=-2\times \frac{41}{20}+2\times \frac{47}{20}-1.

$$y=-\frac{2}{5}$$

Mae’r system wedi’i datrys nawr.

$$x=\frac{41}{20} y=-\frac{2}{5} z=\frac{47}{20}$$