Datrys {l}{3x+y-z=27}{x-y+5z=100}{4x+5y-6z=-95}

$$\left. \begin{array} { l } { 3 x + y - z = 27 } \\ { x - y + 5 z = 100 } \\ { 4 x + 5 y - 6 z = - 95 } \end{array} \right.$$

Datrys ar gyfer x, y, z

$$x = \frac{793}{40} = 19\frac{33}{40} = 19.825$$

$$y = -\frac{411}{20} = -20\frac{11}{20} = -20.55$$

$$z = \frac{477}{40} = 11\frac{37}{40} = 11.925$$

Camau Byr wrth Ddefnyddio Amnewid

Datrys 3x+y-z=27 ar gyfer y.

$$y=-3x+z+27$$

Amnewid -3x+z+27 am y yn yr ail a'r trydydd hafaliad.

$$x-\left(-3x+z+27\right)+5z=100 4x+5\left(-3x+z+27\right)-6z=-95$$

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

$$x=-z+\frac{127}{4} z=-11x+230$$

Amnewid -z+\frac{127}{4} am x yn yr hafaliad z=-11x+230.

$$z=-11\left(-z+\frac{127}{4}\right)+230$$

Datrys z=-11\left(-z+\frac{127}{4}\right)+230 ar gyfer z.

$$z=\frac{477}{40}$$

Amnewid \frac{477}{40} am z yn yr hafaliad x=-z+\frac{127}{4}.

$$x=-\frac{477}{40}+\frac{127}{4}$$

Cyfrifo x o x=-\frac{477}{40}+\frac{127}{4}.

$$x=\frac{793}{40}$$

Amnewid \frac{793}{40} am x a \frac{477}{40} am z yn yr hafaliad y=-3x+z+27.

$$y=-3\times \frac{793}{40}+\frac{477}{40}+27$$

Cyfrifo y o y=-3\times \frac{793}{40}+\frac{477}{40}+27.

$$y=-\frac{411}{20}$$

Mae’r system wedi’i datrys nawr.

$$x=\frac{793}{40} y=-\frac{411}{20} z=\frac{477}{40}$$