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

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

Solvi għal x

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika \sqrt{37} b'10x+7y+5.

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

Uża l-propjetà distributtiva biex timmultiplika \sqrt{149} b'6x-y-23.

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

Naqqas 6\sqrt{149}x miż-żewġ naħat.

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

Naqqas 7\sqrt{37}y miż-żewġ naħat.

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

Naqqas 5\sqrt{37} miż-żewġ naħat.

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

Ikkombina t-termini kollha li fihom x.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'10\sqrt{37}-6\sqrt{149}.

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

Meta tiddividi b'10\sqrt{37}-6\sqrt{149} titneħħa l-multiplikazzjoni b'10\sqrt{37}-6\sqrt{149}.

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

Iddividi -\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y-5\sqrt{37} b'10\sqrt{37}-6\sqrt{149}.

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

Solvi għal y

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika \sqrt{37} b'10x+7y+5.

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

Uża l-propjetà distributtiva biex timmultiplika \sqrt{149} b'6x-y-23.

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

Żid \sqrt{149}y maż-żewġ naħat.

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

Naqqas 10\sqrt{37}x miż-żewġ naħat.

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

Naqqas 5\sqrt{37} miż-żewġ naħat.

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

Ikkombina t-termini kollha li fihom y.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'7\sqrt{37}+\sqrt{149}.

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

Meta tiddividi b'7\sqrt{37}+\sqrt{149} titneħħa l-multiplikazzjoni b'7\sqrt{37}+\sqrt{149}.

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

Iddividi 6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x-5\sqrt{37} b'7\sqrt{37}+\sqrt{149}.

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