Whakaoti i te sqrt{37}(10x+7y+5)=sqrt{149}(6x-y-23)

$$\sqrt { 37 } ( 10 x + 7 y + 5 ) = \sqrt { 149 } ( 6 x - y - 23 )$$

Whakaoti mō x

$$x=\frac{\sqrt{5513}y+67y+5\sqrt{5513}+431}{32}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{37} ki te 10x+7y+5.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}=\sqrt{149}\left(6x-y-23\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{149} ki te 6x-y-23.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}=6\sqrt{149}x-\sqrt{149}y-23\sqrt{149}$$

Tangohia te 6\sqrt{149}x mai i ngā taha e rua.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}-6\sqrt{149}x=-\sqrt{149}y-23\sqrt{149}$$

Tangohia te 7\sqrt{37}y mai i ngā taha e rua.

$$10\sqrt{37}x+5\sqrt{37}-6\sqrt{149}x=-\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y$$

Tangohia te 5\sqrt{37} mai i ngā taha e rua.

$$10\sqrt{37}x-6\sqrt{149}x=-\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y-5\sqrt{37}$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(10\sqrt{37}-6\sqrt{149}\right)x=-\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y-5\sqrt{37}$$

He hanga arowhānui tō te whārite.

$$\left(10\sqrt{37}-6\sqrt{149}\right)x=-7\sqrt{37}y-\sqrt{149}y-5\sqrt{37}-23\sqrt{149}$$

Whakawehea ngā taha e rua ki te 10\sqrt{37}-6\sqrt{149}.

$$\frac{\left(10\sqrt{37}-6\sqrt{149}\right)x}{10\sqrt{37}-6\sqrt{149}}=\frac{-7\sqrt{37}y-\sqrt{149}y-5\sqrt{37}-23\sqrt{149}}{10\sqrt{37}-6\sqrt{149}}$$

Mā te whakawehe ki te 10\sqrt{37}-6\sqrt{149} ka wetekia te whakareanga ki te 10\sqrt{37}-6\sqrt{149}.

$$x=\frac{-7\sqrt{37}y-\sqrt{149}y-5\sqrt{37}-23\sqrt{149}}{10\sqrt{37}-6\sqrt{149}}$$

Whakawehe -\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y-5\sqrt{37} ki te 10\sqrt{37}-6\sqrt{149}.

$$x=\frac{\frac{3\sqrt{149}+5\sqrt{37}}{416}\left(7\sqrt{37}y+\sqrt{149}y+5\sqrt{37}+23\sqrt{149}\right)}{2}$$

Whakaoti mō y

$$y=\frac{\sqrt{5513}x-67x+41-3\sqrt{5513}}{32}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{37} ki te 10x+7y+5.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}=\sqrt{149}\left(6x-y-23\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{149} ki te 6x-y-23.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}=6\sqrt{149}x-\sqrt{149}y-23\sqrt{149}$$

Me tāpiri te \sqrt{149}y ki ngā taha e rua.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}+\sqrt{149}y=6\sqrt{149}x-23\sqrt{149}$$

Tangohia te 10\sqrt{37}x mai i ngā taha e rua.

$$7\sqrt{37}y+5\sqrt{37}+\sqrt{149}y=6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x$$

Tangohia te 5\sqrt{37} mai i ngā taha e rua.

$$7\sqrt{37}y+\sqrt{149}y=6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x-5\sqrt{37}$$

Pahekotia ngā kīanga tau katoa e whai ana i te y.

$$\left(7\sqrt{37}+\sqrt{149}\right)y=6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x-5\sqrt{37}$$

He hanga arowhānui tō te whārite.

$$\left(\sqrt{149}+7\sqrt{37}\right)y=6\sqrt{149}x-10\sqrt{37}x-5\sqrt{37}-23\sqrt{149}$$

Whakawehea ngā taha e rua ki te 7\sqrt{37}+\sqrt{149}.

$$\frac{\left(\sqrt{149}+7\sqrt{37}\right)y}{\sqrt{149}+7\sqrt{37}}=\frac{6\sqrt{149}x-10\sqrt{37}x-5\sqrt{37}-23\sqrt{149}}{\sqrt{149}+7\sqrt{37}}$$

Mā te whakawehe ki te 7\sqrt{37}+\sqrt{149} ka wetekia te whakareanga ki te 7\sqrt{37}+\sqrt{149}.

$$y=\frac{6\sqrt{149}x-10\sqrt{37}x-5\sqrt{37}-23\sqrt{149}}{\sqrt{149}+7\sqrt{37}}$$

Whakawehe 6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x-5\sqrt{37} ki te 7\sqrt{37}+\sqrt{149}.

$$y=\frac{\sqrt{5513}x-67x+41-3\sqrt{5513}}{32}$$