Solve (1-sqrt{5})beta=-2alpha

$$( 1 - \sqrt { 5 } ) \beta = - 2 \alpha$$

Solve for α

$$\alpha =\frac{\left(\sqrt{5}-1\right)\beta }{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-\sqrt{5} by \beta .

$$\beta -\sqrt{5}\beta =-2\alpha$$

Swap sides so that all variable terms are on the left hand side.

$$-2\alpha =\beta -\sqrt{5}\beta$$

The equation is in standard form.

$$-2\alpha =-\sqrt{5}\beta +\beta$$

Divide both sides by -2.

$$\frac{-2\alpha }{-2}=\frac{-\sqrt{5}\beta +\beta }{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$\alpha =\frac{-\sqrt{5}\beta +\beta }{-2}$$

Divide \beta -\beta \sqrt{5} by -2.

$$\alpha =\frac{\sqrt{5}\beta -\beta }{2}$$

Solve for β

$$\beta =\frac{\left(\sqrt{5}+1\right)\alpha }{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-\sqrt{5} by \beta .

$$\beta -\sqrt{5}\beta =-2\alpha$$

Combine all terms containing \beta .

$$\left(1-\sqrt{5}\right)\beta =-2\alpha$$

Divide both sides by 1-\sqrt{5}.

$$\frac{\left(1-\sqrt{5}\right)\beta }{1-\sqrt{5}}=-\frac{2\alpha }{1-\sqrt{5}}$$

Dividing by 1-\sqrt{5} undoes the multiplication by 1-\sqrt{5}.

$$\beta =-\frac{2\alpha }{1-\sqrt{5}}$$

Divide -2\alpha by 1-\sqrt{5}.

$$\beta =\frac{\sqrt{5}\alpha +\alpha }{2}$$