Determine the number of solutions for the following system of equations

Question

2x+5y=7
10y=-4x+14
1)Exactly one solution
2)No solutions
3)infinite solutions
4)Exactly 2 solutions

I solved the equations and got
y=7-2X/5
y=-4X+14/10

and I said infinite solutions. Is that correct?

Answer 1

4 x + 10 y = 14 is the first equation times 2
4 x + 10 y = 14 is the second equation

there is a y for any real x, in other words an infinite number of solutions since both equations are for the same line

Answer 2

so what I had is correct.
Thank you for checking and explaining the work!!

Answer 3

You are welcome :)

Answer 4

You only rearranged them.
You solved for y in terms of x

Answer 5

no