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.