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

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

Lahendage ja leidke x

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

Juhised lineaarvõrrandi lahendamiseks

Kasutage distributiivsusomadust, et korrutada \sqrt{37} ja 10x+7y+5.

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

Kasutage distributiivsusomadust, et korrutada -\sqrt{149} ja 6x-y-23.

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

Korrutage -1 ja -1, et leida 1.

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

Korrutage -23 ja -1, et leida 23.

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

Lahutage mõlemast poolest 6\left(-\sqrt{149}\right)x.

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

Korrutage -1 ja 6, et leida -6.

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

Korrutage -6 ja -1, et leida 6.

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

Lahutage mõlemast poolest 7\sqrt{37}y.

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

Lahutage mõlemast poolest 5\sqrt{37}.

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

Kombineerige kõik liikmed, mis sisaldavad x.

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

Võrrand on standardkujul.

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

Jagage mõlemad pooled 10\sqrt{37}+6\sqrt{149}-ga.

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

10\sqrt{37}+6\sqrt{149}-ga jagamine võtab 10\sqrt{37}+6\sqrt{149}-ga korrutamise tagasi.

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

Jagage \sqrt{149}y+23\sqrt{149}-7\sqrt{37}y-5\sqrt{37} väärtusega 10\sqrt{37}+6\sqrt{149}.

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

Lahendage ja leidke y

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

Juhised lineaarvõrrandi lahendamiseks

Kasutage distributiivsusomadust, et korrutada \sqrt{37} ja 10x+7y+5.

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

Kasutage distributiivsusomadust, et korrutada -\sqrt{149} ja 6x-y-23.

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

Korrutage -1 ja -1, et leida 1.

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

Korrutage -23 ja -1, et leida 23.

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

Lahutage mõlemast poolest \sqrt{149}y.

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

Korrutage 6 ja -1, et leida -6.

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

Lahutage mõlemast poolest 10\sqrt{37}x.

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

Lahutage mõlemast poolest 5\sqrt{37}.

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

Kombineerige kõik liikmed, mis sisaldavad y.

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

Võrrand on standardkujul.

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

Jagage mõlemad pooled 7\sqrt{37}-\sqrt{149}-ga.

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

7\sqrt{37}-\sqrt{149}-ga jagamine võtab 7\sqrt{37}-\sqrt{149}-ga korrutamise tagasi.

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

Jagage -6\sqrt{149}x+23\sqrt{149}-10\sqrt{37}x-5\sqrt{37} väärtusega 7\sqrt{37}-\sqrt{149}.

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