Determine is the solution set for the system of equations shown is the empty set contains one point or is infinite x+2y=0; 2x+4y=0

We can use elimination to solve the system:

x+2y=0           Multiply the first equation by negative 2 so we can eliminate
2x+4y=0

-2-4y=0         Add them, -2X+2X= 0, -4Y+4Y= 0
2x+4y=0                   

0=0 

Since 0 is indeed equal to 0 you have INFINITELY MANY SOLUTIONS.

you could also put both equation in slope intercept form and see if the slopes and Y-intercept are the same.