Question

How many solutions does this system of equations have?

A)
exactly one

B)
exactly two

C)
infinitely many

D)
none

Answer 1

Where the two lines intersect is ur solution. So ur system of equations has exactly 1 solution

Answer 2

Simple...

you have: 3x+2y=6 and -4x+5y=15

re-write the equations-->>>

3x+2y=6 into-->>y=
`-(3)/(2) x+3`

and

-4x+5y=15 into-->>
`y= (4)/(5) x+3`

Set them equal to each other to solve for x-->>


`- (3)/(2) x+3= (4)/(5) x+3`

x=0

Now plug in x...to solve for y...


`- (3)/(2) (0)+3= (4)/(5) (0)+3`

3=3

(0,3)

Thus, your answer, A.