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=$-\frac{3}{2} x+3$

and

-4x+5y=15 into-->>$y= \frac{4}{5} x+3$

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

$- \frac{3}{2} x+3= \frac{4}{5} x+3$

x=0

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

$- \frac{3}{2} (0)+3= \frac{4}{5} (0)+3$

3=3

(0,3)

Thus, your answer, A.