## Answer :

**Answer: D. consistent and independent**

**Step-by-step explanation:**

**The given system is **[tex]2y-3x=9\\4y+3x=12[/tex]

When we compare the coefficients of the corresponding variables of both the equations we get,

For y, [tex]\frac{2}{4}=\frac{1}{2}[/tex]

For x, [tex]\frac{-3}{3}=-1[/tex]

And [tex]\frac{1}{2}\neq-1[/tex],

⇒ The system in independent.

Therefore the system has one unique solution.

Since, if a system has a unique solution then the system is consistent .

**Therefore, the system is consistent and independent.**