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

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

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{37} by 10x+7y+5.

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

Use the distributive property to multiply \sqrt{149} by 6x-y-23.

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

Subtract 6\sqrt{149}x from both sides.

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

Subtract 7\sqrt{37}y from both sides.

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

Subtract 5\sqrt{37} from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 10\sqrt{37}-6\sqrt{149}.

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

Dividing by 10\sqrt{37}-6\sqrt{149} undoes the multiplication by 10\sqrt{37}-6\sqrt{149}.

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

Divide -\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y-5\sqrt{37} by 10\sqrt{37}-6\sqrt{149}.

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

Solve for y

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

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{37} by 10x+7y+5.

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

Use the distributive property to multiply \sqrt{149} by 6x-y-23.

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

Add \sqrt{149}y to both sides.

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

Subtract 10\sqrt{37}x from both sides.

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

Subtract 5\sqrt{37} from both sides.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 7\sqrt{37}+\sqrt{149}.

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

Dividing by 7\sqrt{37}+\sqrt{149} undoes the multiplication by 7\sqrt{37}+\sqrt{149}.

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

Divide 6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x-5\sqrt{37} by 7\sqrt{37}+\sqrt{149}.

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