Answer:
The correct options are:
3x - 4y = 15
15x - 20y = 75
(fourth option, counting fom the top)
5x + 6y = 20
-10x - 12y = -40
(last option)
Explanation:
A system of linear equations has infinitely many solutions if and only if both equations define the same line.
Then we need to see which option describes twice the same line.
From the given options, the two with infinitely many solutions are:
3x - 4y = 15
15x - 20y = 75
How we check that? remember that we can multiply (or divide) both sides of an equation by the same number, and the equation remains unchanged.
So, if we take the first equation and multiply both sides by 5, we get:
5*(3x - 4y) = 5*15
15x - 20y = 75
Which is the same as the other equation, so both equations describe the same line.
The other system is the last one:
5x + 6y = 20
-10x - 12y = -40
If we take the first equation and multiply both sides by -2, we get:
-2*(5x + 6y) = -2*20
-10x - 12y = -40
So, again, both equations describe the same line.