Question

Which of the following equations results in infinitely many solutions?

7y + 15 - 2y = 7(y + 3)
7y +3-2y = 5(y + 3)
7y + 15 = 5(y + 3)
7y + 15 - 2y = 5(y + 3)

Answer 1

7y + 15 - 2y = 5(y + 3)

Explanation:

So two equations have infinitely many solutions, when they are exactly the same equation, in their most simplified form, for example: 2x = 3x-x which simplifies to 2x=2x. So in the options, three of the options have the same equation on the right side, so I'll distribute the 5.
`5(y+3) = 5y+15`. Now let's look at the options:

7y + 3-2y

5y+3 (this is not the same as 5y + 15)

7y + 15 (this is not the same as 5y + 15)

7y + 15 - 2y

5y + 15 = 5y + 15 (this is the same)