Whakaoti i te x-2/frac{4{3}-2}=y+4/frac{2{3}+4}

$$\frac { x - 2 } { \frac { 4 } { 3 } - 2 } = \frac { y + 4 } { \frac { 2 } { 3 } + 4 }$$

Whakaoti mō x

$$x=\frac{10-y}{7}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 2 i te \frac{4}{3}, ka -\frac{2}{3}.

$$\frac{x-2}{-\frac{2}{3}}=\frac{y+4}{\frac{2}{3}+4}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-x+2}{\frac{2}{3}}=\frac{y+4}{\frac{2}{3}+4}$$

Tāpirihia te \frac{2}{3} ki te 4, ka \frac{14}{3}.

$$\frac{-x+2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

Whakawehea ia wā o -x+2 ki te \frac{2}{3}, kia riro ko \frac{-x}{\frac{2}{3}}+\frac{2}{\frac{2}{3}}.

$$\frac{-x}{\frac{2}{3}}+\frac{2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

Whakawehea te -x ki te \frac{2}{3}, kia riro ko -\frac{3}{2}x.

$$-\frac{3}{2}x+\frac{2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

Whakawehe 2 ki te \frac{2}{3} mā te whakarea 2 ki te tau huripoki o \frac{2}{3}.

$$-\frac{3}{2}x+2\times \frac{3}{2}=\frac{y+4}{\frac{14}{3}}$$

Whakareatia te 2 ki te \frac{3}{2}, ka 3.

$$-\frac{3}{2}x+3=\frac{y+4}{\frac{14}{3}}$$

Whakawehea ia wā o y+4 ki te \frac{14}{3}, kia riro ko \frac{y}{\frac{14}{3}}+\frac{4}{\frac{14}{3}}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+\frac{4}{\frac{14}{3}}$$

Whakawehe 4 ki te \frac{14}{3} mā te whakarea 4 ki te tau huripoki o \frac{14}{3}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+4\times \frac{3}{14}$$

Whakareatia te 4 ki te \frac{3}{14}, ka \frac{6}{7}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+\frac{6}{7}$$

Tangohia te 3 mai i ngā taha e rua.

$$-\frac{3}{2}x=\frac{y}{\frac{14}{3}}+\frac{6}{7}-3$$

Tangohia te 3 i te \frac{6}{7}, ka -\frac{15}{7}.

$$-\frac{3}{2}x=\frac{y}{\frac{14}{3}}-\frac{15}{7}$$

He hanga arowhānui tō te whārite.

$$-\frac{3}{2}x=\frac{3y}{14}-\frac{15}{7}$$

Whakawehea ngā taha e rua o te whārite ki te -\frac{3}{2}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-\frac{3}{2}x}{-\frac{3}{2}}=\frac{\frac{3y}{14}-\frac{15}{7}}{-\frac{3}{2}}$$

Mā te whakawehe ki te -\frac{3}{2} ka wetekia te whakareanga ki te -\frac{3}{2}.

$$x=\frac{\frac{3y}{14}-\frac{15}{7}}{-\frac{3}{2}}$$

Whakawehe -\frac{15}{7}+\frac{3y}{14} ki te -\frac{3}{2} mā te whakarea -\frac{15}{7}+\frac{3y}{14} ki te tau huripoki o -\frac{3}{2}.

$$x=\frac{10-y}{7}$$

Whakaoti mō y

$$y=10-7x$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 2 i te \frac{4}{3}, ka -\frac{2}{3}.

$$\frac{x-2}{-\frac{2}{3}}=\frac{y+4}{\frac{2}{3}+4}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-x+2}{\frac{2}{3}}=\frac{y+4}{\frac{2}{3}+4}$$

Tāpirihia te \frac{2}{3} ki te 4, ka \frac{14}{3}.

$$\frac{-x+2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

Whakawehea ia wā o -x+2 ki te \frac{2}{3}, kia riro ko \frac{-x}{\frac{2}{3}}+\frac{2}{\frac{2}{3}}.

$$\frac{-x}{\frac{2}{3}}+\frac{2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

Whakawehea te -x ki te \frac{2}{3}, kia riro ko -\frac{3}{2}x.

$$-\frac{3}{2}x+\frac{2}{\frac{2}{3}}=\frac{y+4}{\frac{14}{3}}$$

Whakawehe 2 ki te \frac{2}{3} mā te whakarea 2 ki te tau huripoki o \frac{2}{3}.

$$-\frac{3}{2}x+2\times \frac{3}{2}=\frac{y+4}{\frac{14}{3}}$$

Whakareatia te 2 ki te \frac{3}{2}, ka 3.

$$-\frac{3}{2}x+3=\frac{y+4}{\frac{14}{3}}$$

Whakawehea ia wā o y+4 ki te \frac{14}{3}, kia riro ko \frac{y}{\frac{14}{3}}+\frac{4}{\frac{14}{3}}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+\frac{4}{\frac{14}{3}}$$

Whakawehe 4 ki te \frac{14}{3} mā te whakarea 4 ki te tau huripoki o \frac{14}{3}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+4\times \frac{3}{14}$$

Whakareatia te 4 ki te \frac{3}{14}, ka \frac{6}{7}.

$$-\frac{3}{2}x+3=\frac{y}{\frac{14}{3}}+\frac{6}{7}$$

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

$$\frac{y}{\frac{14}{3}}+\frac{6}{7}=-\frac{3}{2}x+3$$

Tangohia te \frac{6}{7} mai i ngā taha e rua.

$$\frac{y}{\frac{14}{3}}=-\frac{3}{2}x+3-\frac{6}{7}$$

Tangohia te \frac{6}{7} i te 3, ka \frac{15}{7}.

$$\frac{y}{\frac{14}{3}}=-\frac{3}{2}x+\frac{15}{7}$$

He hanga arowhānui tō te whārite.

$$\frac{3}{14}y=-\frac{3x}{2}+\frac{15}{7}$$

Whakawehea ngā taha e rua o te whārite ki te \frac{3}{14}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{3}{14}y}{\frac{3}{14}}=\frac{-\frac{3x}{2}+\frac{15}{7}}{\frac{3}{14}}$$

Mā te whakawehe ki te \frac{3}{14} ka wetekia te whakareanga ki te \frac{3}{14}.

$$y=\frac{-\frac{3x}{2}+\frac{15}{7}}{\frac{3}{14}}$$

Whakawehe -\frac{3x}{2}+\frac{15}{7} ki te \frac{3}{14} mā te whakarea -\frac{3x}{2}+\frac{15}{7} ki te tau huripoki o \frac{3}{14}.

$$y=10-7x$$