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.
