Solve x/y=frac{1+sqrt{5}}{2}

$$\frac { x } { y } = \frac { 1 + \sqrt { 5 } } { 2 }$$

Solve for x

$$x=\frac{\left(\sqrt{5}+1\right)y}{2}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2x=y\left(1+\sqrt{5}\right)$$

Use the distributive property to multiply y by 1+\sqrt{5}.

$$2x=y+y\sqrt{5}$$

The equation is in standard form.

$$2x=\sqrt{5}y+y$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{\sqrt{5}y+y}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{\sqrt{5}y+y}{2}$$

Divide y+y\sqrt{5} by 2.

$$x=\frac{\left(\sqrt{5}+1\right)y}{2}$$

Solve for y

$$y=\frac{\left(\sqrt{5}-1\right)x}{2}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2x=y\left(1+\sqrt{5}\right)$$

Use the distributive property to multiply y by 1+\sqrt{5}.

$$2x=y+y\sqrt{5}$$

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

$$y+y\sqrt{5}=2x$$

Combine all terms containing y.

$$\left(1+\sqrt{5}\right)y=2x$$

The equation is in standard form.

$$\left(\sqrt{5}+1\right)y=2x$$

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

$$\frac{\left(\sqrt{5}+1\right)y}{\sqrt{5}+1}=\frac{2x}{\sqrt{5}+1}$$

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

$$y=\frac{2x}{\sqrt{5}+1}$$

Divide 2x by 1+\sqrt{5}.

$$y=\frac{\left(\sqrt{5}-1\right)x}{2}$$

Variable y cannot be equal to 0.

$$y=\frac{\left(\sqrt{5}-1\right)x}{2}\text{, }y\neq 0$$