How many solutions does this system have?

2x + y = 3

6x = 9 - 3y

The given system of equation is:

2x + y = 3 ⇒ y=3-2x Subtract 2x from each side.

Next step is to plug in 3-2x form y into the second equation. So,

6x = 9 - 3y

6x=9-3 (3-2x)

6x=9-9+6x By distributing property.

6x=6x

6x-6x=6x-6x Subtract 6x from each sides.

0=0

From the above result notice that x has vanish and we are left with 0=0 which is correct.

Hence, the given system has infinite number of solutions.