Question

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

Answer 1

Answer: B. exactly one

Explanation:

The given system of linear equations :

`3x+2y=6------------(1)\\\\ -4x+5y=15----------------(2)`

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

`(3)/(-4)` ,
`(2)/(5)`

But
`(3)/(-4)\\eq (2)/(5)`

⇒ 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