Whakaoti i te (x-y)+(y-1)i=(2x+3y)+(2y+1)i

$$( x - y ) + ( y - 1 ) i = ( 2 x + 3 y ) + ( 2 y + 1 ) i$$

Whakaoti mō x

$$x=\left(-4-i\right)y-2i$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te y-1 ki te i.

$$x-y+iy-i=2x+3y+\left(2y+1\right)i$$

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

$$x+\left(-1+i\right)y-i=2x+3y+\left(2y+1\right)i$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y+1 ki te i.

$$x+\left(-1+i\right)y-i=2x+3y+2iy+i$$

Pahekotia te 3y me 2iy, ka \left(3+2i\right)y.

$$x+\left(-1+i\right)y-i=2x+\left(3+2i\right)y+i$$

Tangohia te 2x mai i ngā taha e rua.

$$x+\left(-1+i\right)y-i-2x=\left(3+2i\right)y+i$$

Pahekotia te x me -2x, ka -x.

$$-x+\left(-1+i\right)y-i=\left(3+2i\right)y+i$$

Tangohia te \left(-1+i\right)y mai i ngā taha e rua.

$$-x-i=\left(3+2i\right)y+i-\left(-1+i\right)y$$

Pahekotia te \left(3+2i\right)y me \left(1-i\right)y, ka \left(4+i\right)y.

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

Me tāpiri te i ki ngā taha e rua.

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

Tāpirihia te i ki te i, ka 2i.

$$-x=\left(4+i\right)y+2i$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x}{-1}=\frac{\left(4+i\right)y+2i}{-1}$$

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

$$x=\frac{\left(4+i\right)y+2i}{-1}$$

Whakawehe \left(4+i\right)y+2i ki te -1.

$$x=\left(-4-i\right)y-2i$$

Whakaoti mō y

$$y=\left(-\frac{4}{17}+\frac{1}{17}i\right)x+\left(-\frac{2}{17}-\frac{8}{17}i\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te y-1 ki te i.

$$x-y+iy-i=2x+3y+\left(2y+1\right)i$$

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

$$x+\left(-1+i\right)y-i=2x+3y+\left(2y+1\right)i$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y+1 ki te i.

$$x+\left(-1+i\right)y-i=2x+3y+2iy+i$$

Pahekotia te 3y me 2iy, ka \left(3+2i\right)y.

$$x+\left(-1+i\right)y-i=2x+\left(3+2i\right)y+i$$

Tangohia te \left(3+2i\right)y mai i ngā taha e rua.

$$x+\left(-1+i\right)y-i-\left(3+2i\right)y=2x+i$$

Pahekotia te \left(-1+i\right)y me \left(-3-2i\right)y, ka \left(-4-i\right)y.

$$x+\left(-4-i\right)y-i=2x+i$$

Tangohia te x mai i ngā taha e rua.

$$\left(-4-i\right)y-i=2x+i-x$$

Pahekotia te 2x me -x, ka x.

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

Me tāpiri te i ki ngā taha e rua.

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

Tāpirihia te i ki te i, ka 2i.

$$\left(-4-i\right)y=x+2i$$

Whakawehea ngā taha e rua ki te -4-i.

$$\frac{\left(-4-i\right)y}{-4-i}=\frac{x+2i}{-4-i}$$

Mā te whakawehe ki te -4-i ka wetekia te whakareanga ki te -4-i.

$$y=\frac{x+2i}{-4-i}$$

Whakawehe x+2i ki te -4-i.

$$y=\left(-\frac{4}{17}+\frac{1}{17}i\right)x+\left(-\frac{2}{17}-\frac{8}{17}i\right)$$