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

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

Atrast x

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

Lineāra vienādojuma risināšanas darbības

Izmantojiet distributīvo īpašību, lai reizinātu \sqrt{37} ar 10x+7y+5.

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

Izmantojiet distributīvo īpašību, lai reizinātu -\sqrt{149} ar 6x-y-23.

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

Reiziniet -1 un -1, lai iegūtu 1.

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

Reiziniet -23 un -1, lai iegūtu 23.

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

Atņemiet 6\left(-\sqrt{149}\right)x no abām pusēm.

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

Reiziniet -1 un 6, lai iegūtu -6.

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

Reiziniet -6 un -1, lai iegūtu 6.

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

Atņemiet 7\sqrt{37}y no abām pusēm.

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

Atņemiet 5\sqrt{37} no abām pusēm.

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

Savelciet visus locekļus, kuros ir x.

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

Vienādojums ir standarta formā.

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

Daliet abas puses ar 10\sqrt{37}+6\sqrt{149}.

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

Dalīšana ar 10\sqrt{37}+6\sqrt{149} atsauc reizināšanu ar 10\sqrt{37}+6\sqrt{149}.

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

Daliet \sqrt{149}y+23\sqrt{149}-7\sqrt{37}y-5\sqrt{37} ar 10\sqrt{37}+6\sqrt{149}.

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

Atrast y

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

Lineāra vienādojuma risināšanas darbības

Izmantojiet distributīvo īpašību, lai reizinātu \sqrt{37} ar 10x+7y+5.

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

Izmantojiet distributīvo īpašību, lai reizinātu -\sqrt{149} ar 6x-y-23.

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

Reiziniet -1 un -1, lai iegūtu 1.

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

Reiziniet -23 un -1, lai iegūtu 23.

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

Atņemiet \sqrt{149}y no abām pusēm.

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

Reiziniet 6 un -1, lai iegūtu -6.

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

Atņemiet 10\sqrt{37}x no abām pusēm.

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

Atņemiet 5\sqrt{37} no abām pusēm.

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

Savelciet visus locekļus, kuros ir y.

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

Vienādojums ir standarta formā.

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

Daliet abas puses ar 7\sqrt{37}-\sqrt{149}.

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

Dalīšana ar 7\sqrt{37}-\sqrt{149} atsauc reizināšanu ar 7\sqrt{37}-\sqrt{149}.

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

Daliet -6\sqrt{149}x+23\sqrt{149}-10\sqrt{37}x-5\sqrt{37} ar 7\sqrt{37}-\sqrt{149}.

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