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

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

Lahendage ja leidke x

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

Juhised lineaarvõrrandi lahendamiseks

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

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

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

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

Lahutage mõlemast poolest 6\sqrt{149}x.

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

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.

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

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

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

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

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

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

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

Lahendage ja leidke y

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

Juhised lineaarvõrrandi lahendamiseks

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

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

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

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

Liitke \sqrt{149}y mõlemale poolele.

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

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.

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

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

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

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

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

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

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