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

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

Réitigh do x.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun \sqrt{37} a mhéadú faoi 10x+7y+5.

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

Úsáid an t-airí dáileach chun -\sqrt{149} a mhéadú faoi 6x-y-23.

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

Méadaigh -1 agus -1 chun 1 a fháil.

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

Méadaigh -23 agus -1 chun 23 a fháil.

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

Bain 6\left(-\sqrt{149}\right)x ón dá thaobh.

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

Méadaigh -1 agus 6 chun -6 a fháil.

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

Méadaigh -6 agus -1 chun 6 a fháil.

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

Bain 7\sqrt{37}y ón dá thaobh.

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

Bain 5\sqrt{37} ón dá thaobh.

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

Comhcheangail na téarmaí ar fad ina bhfuil x.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi 10\sqrt{37}+6\sqrt{149}.

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

Má roinntear é faoi 10\sqrt{37}+6\sqrt{149} cuirtear an iolrúchán faoi 10\sqrt{37}+6\sqrt{149} ar ceal.

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

Roinn \sqrt{149}y+23\sqrt{149}-7\sqrt{37}y-5\sqrt{37} faoi 10\sqrt{37}+6\sqrt{149}.

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

Réitigh do y.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun \sqrt{37} a mhéadú faoi 10x+7y+5.

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

Úsáid an t-airí dáileach chun -\sqrt{149} a mhéadú faoi 6x-y-23.

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

Méadaigh -1 agus -1 chun 1 a fháil.

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

Méadaigh -23 agus -1 chun 23 a fháil.

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

Bain \sqrt{149}y ón dá thaobh.

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

Méadaigh 6 agus -1 chun -6 a fháil.

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

Bain 10\sqrt{37}x ón dá thaobh.

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

Bain 5\sqrt{37} ón dá thaobh.

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

Comhcheangail na téarmaí ar fad ina bhfuil y.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi 7\sqrt{37}-\sqrt{149}.

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

Má roinntear é faoi 7\sqrt{37}-\sqrt{149} cuirtear an iolrúchán faoi 7\sqrt{37}-\sqrt{149} ar ceal.

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

Roinn -6\sqrt{149}x+23\sqrt{149}-10\sqrt{37}x-5\sqrt{37} faoi 7\sqrt{37}-\sqrt{149}.

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