Solve 2x-ysqrt{3}+12=xsqrt{12}+y

$$2x-y \sqrt{ 3 } +12=x \sqrt{ 12 } +y$$

Solve for x

$$x=-\frac{\sqrt{3}y}{2}-y+3\sqrt{3}+3$$

Steps for Solving Linear Equation

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2x-y\sqrt{3}+12=x\times 2\sqrt{3}+y$$

Subtract x\times 2\sqrt{3} from both sides.

$$2x-y\sqrt{3}+12-x\times 2\sqrt{3}=y$$

Multiply -1 and 2 to get -2.

$$2x-y\sqrt{3}+12-2x\sqrt{3}=y$$

Add y\sqrt{3} to both sides.

$$2x+12-2x\sqrt{3}=y+y\sqrt{3}$$

Subtract 12 from both sides.

$$2x-2x\sqrt{3}=y+y\sqrt{3}-12$$

Combine all terms containing x.

$$\left(2-2\sqrt{3}\right)x=y+y\sqrt{3}-12$$

The equation is in standard form.

$$\left(2-2\sqrt{3}\right)x=\sqrt{3}y+y-12$$

Divide both sides by 2-2\sqrt{3}.

$$\frac{\left(2-2\sqrt{3}\right)x}{2-2\sqrt{3}}=\frac{\sqrt{3}y+y-12}{2-2\sqrt{3}}$$

Dividing by 2-2\sqrt{3} undoes the multiplication by 2-2\sqrt{3}.

$$x=\frac{\sqrt{3}y+y-12}{2-2\sqrt{3}}$$

Divide y+y\sqrt{3}-12 by 2-2\sqrt{3}.

$$x=-\frac{\sqrt{3}y}{2}-y+3\sqrt{3}+3$$

Solve for y

$$y=2\left(\sqrt{3}x-2x+3\sqrt{3}-3\right)$$

Steps for Solving Linear Equation

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2x-y\sqrt{3}+12=x\times 2\sqrt{3}+y$$

Subtract y from both sides.

$$2x-y\sqrt{3}+12-y=x\times 2\sqrt{3}$$

Subtract 12 from both sides.

$$2x-y\sqrt{3}-y=x\times 2\sqrt{3}-12$$

Subtract 2x from both sides.

$$-y\sqrt{3}-y=x\times 2\sqrt{3}-12-2x$$

Combine all terms containing y.

$$\left(-\sqrt{3}-1\right)y=x\times 2\sqrt{3}-12-2x$$

The equation is in standard form.

$$\left(-\sqrt{3}-1\right)y=2\sqrt{3}x-2x-12$$

Divide both sides by -\sqrt{3}-1.

$$\frac{\left(-\sqrt{3}-1\right)y}{-\sqrt{3}-1}=\frac{2\sqrt{3}x-2x-12}{-\sqrt{3}-1}$$

Dividing by -\sqrt{3}-1 undoes the multiplication by -\sqrt{3}-1.

$$y=\frac{2\sqrt{3}x-2x-12}{-\sqrt{3}-1}$$

Divide 2\sqrt{3}x-12-2x by -\sqrt{3}-1.

$$y=\left(1-\sqrt{3}\right)\left(\sqrt{3}x-x-6\right)$$