Whakaoti i te 40/56x+(23y-10y-x)*40/74=203*40/1000

$$\frac { 40 } { 56 } x + ( 23 y - 10 y - x ) \times \frac { 40 } { 74 } = 203 \times \frac { 40 } { 1000 }$$

Whakaoti mō x

$$x=-\frac{364y}{9}+\frac{52577}{1125}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{40}{56} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$\frac{5}{7}x+\left(23y-10y-x\right)\times \frac{40}{74}=203\times \frac{40}{1000}$$

Pahekotia te 23y me -10y, ka 13y.

$$\frac{5}{7}x+\left(13y-x\right)\times \frac{40}{74}=203\times \frac{40}{1000}$$

Whakahekea te hautanga \frac{40}{74} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{5}{7}x+\left(13y-x\right)\times \frac{20}{37}=203\times \frac{40}{1000}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 13y-x ki te \frac{20}{37}.

$$\frac{5}{7}x+\frac{260}{37}y-\frac{20}{37}x=203\times \frac{40}{1000}$$

Pahekotia te \frac{5}{7}x me -\frac{20}{37}x, ka \frac{45}{259}x.

$$\frac{45}{259}x+\frac{260}{37}y=203\times \frac{40}{1000}$$

Whakahekea te hautanga \frac{40}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$\frac{45}{259}x+\frac{260}{37}y=203\times \frac{1}{25}$$

Whakareatia te 203 ki te \frac{1}{25}, ka \frac{203}{25}.

$$\frac{45}{259}x+\frac{260}{37}y=\frac{203}{25}$$

Tangohia te \frac{260}{37}y mai i ngā taha e rua.

$$\frac{45}{259}x=\frac{203}{25}-\frac{260}{37}y$$

He hanga arowhānui tō te whārite.

$$\frac{45}{259}x=-\frac{260y}{37}+\frac{203}{25}$$

Whakawehea ngā taha e rua o te whārite ki te \frac{45}{259}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{45}{259}x}{\frac{45}{259}}=\frac{-\frac{260y}{37}+\frac{203}{25}}{\frac{45}{259}}$$

Mā te whakawehe ki te \frac{45}{259} ka wetekia te whakareanga ki te \frac{45}{259}.

$$x=\frac{-\frac{260y}{37}+\frac{203}{25}}{\frac{45}{259}}$$

Whakawehe \frac{203}{25}-\frac{260y}{37} ki te \frac{45}{259} mā te whakarea \frac{203}{25}-\frac{260y}{37} ki te tau huripoki o \frac{45}{259}.

$$x=-\frac{364y}{9}+\frac{52577}{1125}$$

Whakaoti mō y

$$y=-\frac{9x}{364}+\frac{7511}{6500}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{40}{56} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$\frac{5}{7}x+\left(23y-10y-x\right)\times \frac{40}{74}=203\times \frac{40}{1000}$$

Pahekotia te 23y me -10y, ka 13y.

$$\frac{5}{7}x+\left(13y-x\right)\times \frac{40}{74}=203\times \frac{40}{1000}$$

Whakahekea te hautanga \frac{40}{74} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{5}{7}x+\left(13y-x\right)\times \frac{20}{37}=203\times \frac{40}{1000}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 13y-x ki te \frac{20}{37}.

$$\frac{5}{7}x+\frac{260}{37}y-\frac{20}{37}x=203\times \frac{40}{1000}$$

Pahekotia te \frac{5}{7}x me -\frac{20}{37}x, ka \frac{45}{259}x.

$$\frac{45}{259}x+\frac{260}{37}y=203\times \frac{40}{1000}$$

Whakahekea te hautanga \frac{40}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$\frac{45}{259}x+\frac{260}{37}y=203\times \frac{1}{25}$$

Whakareatia te 203 ki te \frac{1}{25}, ka \frac{203}{25}.

$$\frac{45}{259}x+\frac{260}{37}y=\frac{203}{25}$$

Tangohia te \frac{45}{259}x mai i ngā taha e rua.

$$\frac{260}{37}y=\frac{203}{25}-\frac{45}{259}x$$

He hanga arowhānui tō te whārite.

$$\frac{260}{37}y=-\frac{45x}{259}+\frac{203}{25}$$

Whakawehea ngā taha e rua o te whārite ki te \frac{260}{37}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{260}{37}y}{\frac{260}{37}}=\frac{-\frac{45x}{259}+\frac{203}{25}}{\frac{260}{37}}$$

Mā te whakawehe ki te \frac{260}{37} ka wetekia te whakareanga ki te \frac{260}{37}.

$$y=\frac{-\frac{45x}{259}+\frac{203}{25}}{\frac{260}{37}}$$

Whakawehe \frac{203}{25}-\frac{45x}{259} ki te \frac{260}{37} mā te whakarea \frac{203}{25}-\frac{45x}{259} ki te tau huripoki o \frac{260}{37}.

$$y=-\frac{9x}{364}+\frac{7511}{6500}$$