Datrys {l}{2x+4y-12z=6}{x+y+2z=26}{3x-3y+3z=3}

$$\left. \begin{array} { l } { 2 x + 4 y - 12 z = 6 } \\ { x + y + 2 z = 26 } \\ { 3 x - 3 y + 3 z = 3 } \end{array} \right.$$

Datrys ar gyfer x, y, z

$$x = \frac{123}{17} = 7\frac{4}{17} \approx 7.235294118$$

$$y = \frac{177}{17} = 10\frac{7}{17} \approx 10.411764706$$

$$z = \frac{71}{17} = 4\frac{3}{17} \approx 4.176470588$$

Camau Byr wrth Ddefnyddio Amnewid

Newid trefn yr hafaliadau.

$$x+y+2z=26 2x+4y-12z=6 3x-3y+3z=3$$

Datrys x+y+2z=26 ar gyfer x.

$$x=-y-2z+26$$

Amnewid -y-2z+26 am x yn yr ail a'r trydydd hafaliad.

$$2\left(-y-2z+26\right)+4y-12z=6 3\left(-y-2z+26\right)-3y+3z=3$$

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

$$y=-23+8z z=25-2y$$

Amnewid -23+8z am y yn yr hafaliad z=25-2y.

$$z=25-2\left(-23+8z\right)$$

Datrys z=25-2\left(-23+8z\right) ar gyfer z.

$$z=\frac{71}{17}$$

Amnewid \frac{71}{17} am z yn yr hafaliad y=-23+8z.

$$y=-23+8\times \frac{71}{17}$$

Cyfrifo y o y=-23+8\times \frac{71}{17}.

$$y=\frac{177}{17}$$

Amnewid \frac{177}{17} am y a \frac{71}{17} am z yn yr hafaliad x=-y-2z+26.

$$x=-\frac{177}{17}-2\times \frac{71}{17}+26$$

Cyfrifo x o x=-\frac{177}{17}-2\times \frac{71}{17}+26.

$$x=\frac{123}{17}$$

Mae’r system wedi’i datrys nawr.

$$x=\frac{123}{17} y=\frac{177}{17} z=\frac{71}{17}$$