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

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

I-solve ang x

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

Mga Hakbang sa Pagso-solve ng Linear Equation

Gamitin ang distributive property para i-multiply ang \sqrt{37} gamit ang 10x+7y+5.

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

Gamitin ang distributive property para i-multiply ang -\sqrt{149} gamit ang 6x-y-23.

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

I-multiply ang -1 at -1 para makuha ang 1.

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

I-multiply ang -23 at -1 para makuha ang 23.

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

I-subtract ang 6\left(-\sqrt{149}\right)x mula sa magkabilang dulo.

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

I-multiply ang -1 at 6 para makuha ang -6.

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

I-multiply ang -6 at -1 para makuha ang 6.

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

I-subtract ang 7\sqrt{37}y mula sa magkabilang dulo.

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

I-subtract ang 5\sqrt{37} mula sa magkabilang dulo.

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

Pagsamahin ang lahat ng term na naglalaman ng x.

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

Ang equation ay nasa standard form.

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

I-divide ang magkabilang dulo ng equation gamit ang 10\sqrt{37}+6\sqrt{149}.

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

Kapag na-divide gamit ang 10\sqrt{37}+6\sqrt{149}, ma-a-undo ang multiplication gamit ang 10\sqrt{37}+6\sqrt{149}.

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

I-divide ang \sqrt{149}y+23\sqrt{149}-7\sqrt{37}y-5\sqrt{37} gamit ang 10\sqrt{37}+6\sqrt{149}.

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

I-solve ang y

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

Mga Hakbang sa Pagso-solve ng Linear Equation

Gamitin ang distributive property para i-multiply ang \sqrt{37} gamit ang 10x+7y+5.

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

Gamitin ang distributive property para i-multiply ang -\sqrt{149} gamit ang 6x-y-23.

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

I-multiply ang -1 at -1 para makuha ang 1.

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

I-multiply ang -23 at -1 para makuha ang 23.

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

I-subtract ang \sqrt{149}y mula sa magkabilang dulo.

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

I-multiply ang 6 at -1 para makuha ang -6.

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

I-subtract ang 10\sqrt{37}x mula sa magkabilang dulo.

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

I-subtract ang 5\sqrt{37} mula sa magkabilang dulo.

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

Pagsamahin ang lahat ng term na naglalaman ng y.

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

Ang equation ay nasa standard form.

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

I-divide ang magkabilang dulo ng equation gamit ang 7\sqrt{37}-\sqrt{149}.

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

Kapag na-divide gamit ang 7\sqrt{37}-\sqrt{149}, ma-a-undo ang multiplication gamit ang 7\sqrt{37}-\sqrt{149}.

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

I-divide ang -6\sqrt{149}x+23\sqrt{149}-10\sqrt{37}x-5\sqrt{37} gamit ang 7\sqrt{37}-\sqrt{149}.

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