Question

15)9x + 18y = 0

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of 9 and 18 is 9. Factor out 9 from the left - hand side of the equation $9x + 18y=0$.
We know that $9x=9\times x$ and $18y = 9\times2y$. So, $9x + 18y=9(x + 2y)$.
The equation becomes $9(x + 2y)=0$.

Step2: Solve for x and y relationship

Divide both sides of the equation $9(x + 2y)=0$ by 9. We get $x + 2y=0$.
We can express $x$ in terms of $y$ as $x=- 2y$, or express $y$ in terms of $x$ as $y =-\frac{1}{2}x$. This is the equation of a straight line in slope - intercept form ($y=mx + b$, where $m =-\frac{1}{2}$ and $b = 0$) or in standard form.

Answer:

The simplified form is $x + 2y = 0$ (or equivalent forms like $x=-2y$ or $y=-\frac{1}{2}x$)