Whakaoti i te -7i^8x-4i+y=-5i^19y-4x

$$-7 { i }^{ 8 } x-4i+y = -5 { i }^{ 19 } y-4x$$

Whakaoti mō x

$$x=\left(\frac{1}{3}-\frac{5}{3}i\right)y-\frac{4}{3}i$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te i mā te pū o 8, kia riro ko 1.

$$-7x-4i+y=-5i^{19}y-4x$$

Tātaihia te i mā te pū o 19, kia riro ko -i.

$$-7x-4i+y=-5\left(-i\right)y-4x$$

Whakareatia te -5 ki te -i, ka 5i.

$$-7x-4i+y=5iy-4x$$

Me tāpiri te 4x ki ngā taha e rua.

$$-7x-4i+y+4x=5iy$$

Pahekotia te -7x me 4x, ka -3x.

$$-3x-4i+y=5iy$$

Me tāpiri te 4i ki ngā taha e rua.

$$-3x+y=5iy+4i$$

Tangohia te y mai i ngā taha e rua.

$$-3x=5iy+4i-y$$

Pahekotia te 5iy me -y, ka \left(-1+5i\right)y.

$$-3x=\left(-1+5i\right)y+4i$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x}{-3}=\frac{\left(-1+5i\right)y+4i}{-3}$$

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

$$x=\frac{\left(-1+5i\right)y+4i}{-3}$$

Whakawehe \left(-1+5i\right)y+4i ki te -3.

$$x=\left(\frac{1}{3}-\frac{5}{3}i\right)y-\frac{4}{3}i$$

Whakaoti mō y

$$y=\left(\frac{3}{26}+\frac{15}{26}i\right)x+\left(-\frac{10}{13}+\frac{2}{13}i\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te i mā te pū o 8, kia riro ko 1.

$$-7x-4i+y=-5i^{19}y-4x$$

Tātaihia te i mā te pū o 19, kia riro ko -i.

$$-7x-4i+y=-5\left(-i\right)y-4x$$

Whakareatia te -5 ki te -i, ka 5i.

$$-7x-4i+y=5iy-4x$$

Tangohia te 5iy mai i ngā taha e rua.

$$-7x-4i+y-5iy=-4x$$

Pahekotia te y me -5iy, ka \left(1-5i\right)y.

$$-7x-4i+\left(1-5i\right)y=-4x$$

Me tāpiri te 7x ki ngā taha e rua.

$$-4i+\left(1-5i\right)y=-4x+7x$$

Pahekotia te -4x me 7x, ka 3x.

$$-4i+\left(1-5i\right)y=3x$$

Me tāpiri te 4i ki ngā taha e rua.

$$\left(1-5i\right)y=3x+4i$$

Whakawehea ngā taha e rua ki te 1-5i.

$$\frac{\left(1-5i\right)y}{1-5i}=\frac{3x+4i}{1-5i}$$

Mā te whakawehe ki te 1-5i ka wetekia te whakareanga ki te 1-5i.

$$y=\frac{3x+4i}{1-5i}$$

Whakawehe 3x+4i ki te 1-5i.

$$y=\left(\frac{3}{26}+\frac{15}{26}i\right)x+\left(-\frac{10}{13}+\frac{2}{13}i\right)$$