How many solutions does this system of equations have?

3x+2y =6

-4x+5y=15      a. none   b. exactly one   c. exactly two   d. infinitely many

 B. exactly one

Step-by-step explanation:

The given system of linear equations :

When we find the ratio of the coefficients of the corresponding variable x and y term , we get

 ,

But

⇒ 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

the answer is c. 23/3