Answer: B. exactly one
Step-by-step explanation:
The given system of linear equations :
[tex]3x+2y=6------------(1)\\\\ -4x+5y=15----------------(2)[/tex]
When we find the ratio of the coefficients of the corresponding variable x and y term , we get
[tex]\dfrac{3}{-4}[/tex] , [tex]\dfrac{2}{5}[/tex]
But [tex]\dfrac{3}{-4}\neq \dfrac{2}{5}[/tex]
⇒ System is representing two intersection lines . [if ratio of the coefficients of the corresponding variable x and y term is not equal then they represent intersecting lines.]
⇒System has one unique solution. [Intersecting lines have one solution on plane.]
Hence, the correct answer is B. exactly one
