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

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

Whakaoti mō x

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

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

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

Whakareatia te -1 ki te -1, ka 1.

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

Whakareatia te -23 ki te -1, ka 23.

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

Tangohia te 6\left(-\sqrt{149}\right)x mai i ngā taha e rua.

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

Whakareatia te -1 ki te 6, ka -6.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}-6\left(-1\right)\sqrt{149}x=\sqrt{149}y+23\sqrt{149}$$

Whakareatia te -6 ki te -1, ka 6.

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

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.

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

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

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

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

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

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

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

Whakaoti mō y

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

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

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

Whakareatia te -1 ki te -1, ka 1.

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

Whakareatia te -23 ki te -1, ka 23.

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

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

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

Whakareatia te 6 ki te -1, ka -6.

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

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.

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

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

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

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

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

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

$$y=\frac{\sqrt{149}+7\sqrt{37}}{1664}\left(-6\sqrt{149}x-10\sqrt{37}x+23\sqrt{149}-5\sqrt{37}\right)$$