1. The problem states we start with the equation $$y = - \frac{1}{\sqrt{3}} x$$. 2. You are asked to multiply both sides by $$x$$. This means you multiply each side of the equation by the variable $$x$$. 3. Multiplying, we get: $$xy = - \frac{1}{\sqrt{3}} x \times x = - \frac{1}{\sqrt{3}} x^2$$ 4. So the equation after multiplying both sides by $$x$$ is: $$xy = - \frac{1}{\sqrt{3}} x^2$$ 5. The confusion might be because initially $$y$$ is expressed in terms of $$x$$, and multiplying by $$x$$ affects both sides. 6. Remember, multiplying both sides of an equation by the same well-defined term (here $$x$$) is valid, but be cautious that if $$x=0$$, multiplying could introduce or hide solutions. Summary: Multiplying both sides by $$x$$ changes the original equation to $$xy = - \frac{1}{\sqrt{3}} x^2$$.