Question

2. The lines -2x – 3y = 8 and 4x - 2ay = 9 are parallel. Find the value of a.

Answer 1

`\begin{gathered} \text{If two lines are parallel, then the both lines will have same slope.} \\ \text{the slope from the first equation.} \\ -2x-3y=8 \\ 3y=-2x-8 \\ y=(-2)/(3)x-(8)/(3) \\ \text{Slope }\Rightarrow m=-(2)/(3) \\ \text{Now, from the second equation.} \\ 4x-2ay=9 \\ 2ay=4x-9 \\ y=(4)/(2a)x-(9)/(2a) \\ \text{Slope from this equation is} \\ m=(4)/(2a)=(2)/(a) \\ \text{equate both slope } \\ (2)/(a)=-(2)/(3) \\ a=-3 \end{gathered}`