Ketosis Probs

I am having an extremely hard time getting into ketosis. I eat eggs with cheese for breakfast, a salad equalling 3carbs for lunch, and for dinner I will make grilled chicken or hamburger meat or steak or something similar. Every so often I will make a quesadilla with a low-carb tortilla (5carbs) and cheddar or mozzarella, and I usually have a Diet Hansen's soda with lunch. Every day I am under 20 carbs, and my ketone test strips are reading negative every day.

Is my system just not tolerant? Should I cut back to 10 carbs a day for induction ketosis to finally take place?

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