Whakaoti i te x^2+y^2-2x-8y+17=x^2+y^2+2x-4y+5

$$x ^ { 2 } + y ^ { 2 } - 2 x - 8 y + 17 = x ^ { 2 } + y ^ { 2 } + 2 x - 4 y + 5$$

Whakaoti mō x

$$x=3-y$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te x^{2} mai i ngā taha e rua.

$$x^{2}+y^{2}-2x-8y+17-x^{2}=y^{2}+2x-4y+5$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$y^{2}-2x-8y+17=y^{2}+2x-4y+5$$

Tangohia te 2x mai i ngā taha e rua.

$$y^{2}-2x-8y+17-2x=y^{2}-4y+5$$

Pahekotia te -2x me -2x, ka -4x.

$$y^{2}-4x-8y+17=y^{2}-4y+5$$

Tangohia te y^{2} mai i ngā taha e rua.

$$-4x-8y+17=y^{2}-4y+5-y^{2}$$

Pahekotia te y^{2} me -y^{2}, ka 0.

$$-4x-8y+17=-4y+5$$

Me tāpiri te 8y ki ngā taha e rua.

$$-4x+17=-4y+5+8y$$

Pahekotia te -4y me 8y, ka 4y.

$$-4x+17=4y+5$$

Tangohia te 17 mai i ngā taha e rua.

$$-4x=4y+5-17$$

Tangohia te 17 i te 5, ka -12.

$$-4x=4y-12$$

Whakawehea ngā taha e rua ki te -4.

$$\frac{-4x}{-4}=\frac{4y-12}{-4}$$

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

$$x=\frac{4y-12}{-4}$$

Whakawehe -12+4y ki te -4.

$$x=3-y$$

Whakaoti mō y

$$y=3-x$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te y^{2} mai i ngā taha e rua.

$$x^{2}+y^{2}-2x-8y+17-y^{2}=x^{2}+2x-4y+5$$

Pahekotia te y^{2} me -y^{2}, ka 0.

$$x^{2}-2x-8y+17=x^{2}+2x-4y+5$$

Me tāpiri te 4y ki ngā taha e rua.

$$x^{2}-2x-8y+17+4y=x^{2}+2x+5$$

Pahekotia te -8y me 4y, ka -4y.

$$x^{2}-2x-4y+17=x^{2}+2x+5$$

Tangohia te x^{2} mai i ngā taha e rua.

$$-2x-4y+17=x^{2}+2x+5-x^{2}$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$-2x-4y+17=2x+5$$

Me tāpiri te 2x ki ngā taha e rua.

$$-4y+17=2x+5+2x$$

Pahekotia te 2x me 2x, ka 4x.

$$-4y+17=4x+5$$

Tangohia te 17 mai i ngā taha e rua.

$$-4y=4x+5-17$$

Tangohia te 17 i te 5, ka -12.

$$-4y=4x-12$$

Whakawehea ngā taha e rua ki te -4.

$$\frac{-4y}{-4}=\frac{4x-12}{-4}$$

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

$$y=\frac{4x-12}{-4}$$

Whakawehe -12+4x ki te -4.

$$y=3-x$$