Question 969467
An infinite number of solutions means the same equation.
A is correct.
2x+5y=1   Multiply each term by 3, and you get 6x+15y=3, which is the other equation.

The second one has a solution at x=7 and y=3.

The third one has a solution at x=13 and y=-3

The 4th one has a solution at x=8  y=0.

What you look for are multiples.  In A, I see 2x and 6x  That is a multiple of 3.  Then I look at y.
5y and 15 y, also multiple of 3.  Then I look across the equals sign  1 and 3.  This is the same equation.  

Be careful, however.  If the second were 6x=15y +3, this is not a multiple, because the x and y are on opposite sides of the equals sign.  

x+y=something
x-y = something  Almost always have a solution.  Just add the x s and the y s disappear.


2x + 5y=1
6x+15y+3

Multiply top equation by 3   3{2x+5y=1)    3 * 2x=6x   3(5y)=15y   3*1=3   We distribute the 3 over every term in the equation

6x +15y=3
6x +15y=3  (the bottom equation)

Multiply the top equation by (-1).  This changes all the signs.

-6x-15y=-3
6x +15y =3   Now add
0   + 0  = 0

This means that any x, y pair will work.  Both of these equations describe the same line.   I hope that helps!

I didn't show the solutions for the others, because the first one has an infinite number of solutions.  It can be shown that the others do not.