Hello everyone. I'm having some issues finding all of the solutions to this system:
108z - 4yz - 2z^2 = 0
108y - 2y^2 - 4yz = 0
I've been able to solve it for the 3 of the solutions:
y = 0 and z = 0 (written as the pair (0, 0))
y = 54 and z = 0 (written as the pair (54, 0))
y = 0 and z = 54 (written as the pair (0, 54))
but there is one more solution I haven't been able to get: y = 18 and z = 18 (or (18, 18)). I'm guessing that I'm seriously overthinking this, but I have been working on this for a long time and I don't see how to get that 4th answer (18, 18). Help or some advice for finding this one would be greatly appreciated.
108z - 4yz - 2z^2 = 0
108y - 2y^2 - 4yz = 0
I've been able to solve it for the 3 of the solutions:
y = 0 and z = 0 (written as the pair (0, 0))
y = 54 and z = 0 (written as the pair (54, 0))
y = 0 and z = 54 (written as the pair (0, 54))
but there is one more solution I haven't been able to get: y = 18 and z = 18 (or (18, 18)). I'm guessing that I'm seriously overthinking this, but I have been working on this for a long time and I don't see how to get that 4th answer (18, 18). Help or some advice for finding this one would be greatly appreciated.