Whakaoti i te [3.5Y_{3}+(-9Y_{3})-25Y]-(+2XY-3Y_{3}-5Y)=-2,038.5D_{0}

$$[ 3.5 Y _ { 3 } + ( - 9 Y _ { 3 } ) - 25 Y ] - ( + 2 X Y - 3 Y _ { 3 } - 5 Y ) = - 2,038.5 D _ { 0 }$$

Whakaoti mō D_0

$$D_{0}=\frac{4XY+40Y+5Y_{3}}{4077}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Pahekotia te 3.5Y_{3} me -9Y_{3}, ka -5.5Y_{3}.

$$-5.5Y_{3}-25Y-\left(2XY-3Y_{3}-5Y\right)=-2038.5D_{0}$$

Hei kimi i te tauaro o 2XY-3Y_{3}-5Y, kimihia te tauaro o ia taurangi.

$$-5.5Y_{3}-25Y-2XY+3Y_{3}+5Y=-2038.5D_{0}$$

Pahekotia te -5.5Y_{3} me 3Y_{3}, ka -2.5Y_{3}.

$$-2.5Y_{3}-25Y-2XY+5Y=-2038.5D_{0}$$

Pahekotia te -25Y me 5Y, ka -20Y.

$$-2.5Y_{3}-20Y-2XY=-2038.5D_{0}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-2038.5D_{0}=-2.5Y_{3}-20Y-2XY$$

He hanga arowhānui tō te whārite.

$$-2038.5D_{0}=-2XY-\frac{5Y_{3}}{2}-20Y$$

Whakawehea ngā taha e rua o te whārite ki te -2038.5, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-2038.5D_{0}}{-2038.5}=\frac{-2XY-\frac{5Y_{3}}{2}-20Y}{-2038.5}$$

Mā te whakawehe ki te -2038.5 ka wetekia te whakareanga ki te -2038.5.

$$D_{0}=\frac{-2XY-\frac{5Y_{3}}{2}-20Y}{-2038.5}$$

Whakawehe -\frac{5Y_{3}}{2}-20Y-2XY ki te -2038.5 mā te whakarea -\frac{5Y_{3}}{2}-20Y-2XY ki te tau huripoki o -2038.5.

$$D_{0}=\frac{4XY+40Y+5Y_{3}}{4077}$$

Whakaoti mō X

$$\left\{\begin{matrix}X=-\frac{\frac{5Y_{3}}{2}-\frac{4077D_{0}}{2}+20Y}{2Y}\text{, }&Y\neq 0\\X\in \mathrm{R}\text{, }&Y_{3}=\frac{4077D_{0}}{5}\text{ and }Y=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Pahekotia te 3.5Y_{3} me -9Y_{3}, ka -5.5Y_{3}.

$$-5.5Y_{3}-25Y-\left(2XY-3Y_{3}-5Y\right)=-2038.5D_{0}$$

Hei kimi i te tauaro o 2XY-3Y_{3}-5Y, kimihia te tauaro o ia taurangi.

$$-5.5Y_{3}-25Y-2XY+3Y_{3}+5Y=-2038.5D_{0}$$

Pahekotia te -5.5Y_{3} me 3Y_{3}, ka -2.5Y_{3}.

$$-2.5Y_{3}-25Y-2XY+5Y=-2038.5D_{0}$$

Pahekotia te -25Y me 5Y, ka -20Y.

$$-2.5Y_{3}-20Y-2XY=-2038.5D_{0}$$

Me tāpiri te 2.5Y_{3} ki ngā taha e rua.

$$-20Y-2XY=-2038.5D_{0}+2.5Y_{3}$$

Me tāpiri te 20Y ki ngā taha e rua.

$$-2XY=-2038.5D_{0}+2.5Y_{3}+20Y$$

He hanga arowhānui tō te whārite.

$$\left(-2Y\right)X=\frac{5Y_{3}}{2}-\frac{4077D_{0}}{2}+20Y$$

Whakawehea ngā taha e rua ki te -2Y.

$$\frac{\left(-2Y\right)X}{-2Y}=\frac{\frac{5Y_{3}}{2}-\frac{4077D_{0}}{2}+20Y}{-2Y}$$

Mā te whakawehe ki te -2Y ka wetekia te whakareanga ki te -2Y.

$$X=\frac{\frac{5Y_{3}}{2}-\frac{4077D_{0}}{2}+20Y}{-2Y}$$

Whakawehe -\frac{4077D_{0}}{2}+\frac{5Y_{3}}{2}+20Y ki te -2Y.

$$X=-\frac{5Y_{3}+40Y-4077D_{0}}{4Y}$$