Datrys {l}{{(2x+i)}{(4+3i)}={(5+yi)}}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { {(2 x + i)} {(4 + 3 i)} = {(5 + y i)} }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Datrys ar gyfer x, y, z

$$x=\left(\frac{3}{50}+\frac{2}{25}i\right)a+\left(\frac{2}{5}-\frac{4}{5}i\right)$$

$$y=a$$

$$z=a$$

Camau Byr wrth Ddefnyddio Amnewid

Newid trefn yr hafaliadau.

$$z=y \left(2x+i\right)\left(4+3i\right)=5+yi a=z$$

Amnewid y am z yn yr hafaliad a=z.

$$a=y$$

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

$$x=\frac{2}{5}-\frac{4}{5}i+\left(\frac{3}{50}+\frac{2}{25}i\right)y y=a$$

Amnewid a am y yn yr hafaliad x=\frac{2}{5}-\frac{4}{5}i+\left(\frac{3}{50}+\frac{2}{25}i\right)y.

$$x=\frac{2}{5}-\frac{4}{5}i+\left(\frac{3}{50}+\frac{2}{25}i\right)a$$

Amnewid a am y yn yr hafaliad z=y.

$$z=a$$

Mae’r system wedi’i datrys nawr.

$$x=\frac{2}{5}-\frac{4}{5}i+\left(\frac{3}{50}+\frac{2}{25}i\right)a y=a z=a$$