conflicting answers exist in this same page

That's because the first answer is from a "self taught expert in ancient mysteries", while the second is from a university professor. The first guy is peddling conspiracy theories about the pyramids being 10,000 years old. The second provides a reasonable answer.

Here's a map showing the desertification of Egypt over the last 10,000 years. Yellow shades represent desert and green shades represent vegetation. Solid filled red circles indicate major settlements found in the archaeological record, while circles with red outlines and no fill show settlements that bear signs of having been abandoned at some point in their history. The four panels show Egypt at different time periods, with the dates on the bottom right.

Briefly, during the last glacial maximum around 20,000 years ago, much of the world's fresh water was locked in ice sheets several miles thick that spread across northern latitudes. Northern Africa was a huge desert, about twice as big as the Sahara is today. Beginning with the Holocene around 11,000 years ago, the monsoons shifted northwards, greening the desert from the south, northwards. This is when the first settled communities appear.

The first plate to the left shows Egypt at the start of the Holocene. As the monsoon enters Egypt from the south, the earliest settlements are on the southern border between what are now Egypt and Sudan.

Over the next two panels you can see the further advance of the monsoon northwards. Much of Egypt looks light green, which represents grasslands that were suitable for pasture, but not quite wet enough for farming. The grasslands also supported large herds of deer and other animals. You can see a number of settlements (represented by red dots) spread westwards from the Nile, into what is barren sand dunes today.

The people at this time were mostly hunters and foragers, but this is also when the first domesticated cattle (and later sheep and goats) appear, so it marks the beginning of pastoralism. Probably the period between 9,500 to 7,500 years ago is when we see the transition from a primarily hunting and foraging lifestyle through an increasingly mixed stage, towards widespread pastoralism.

Around 7,000 years ago, agriculture first appears in the region of the Faiyum Valley (the area just west of the Nile, south of the delta). It spreads eastwards towards the Nile, and then follows the track of the Nile north and south, in a belt that's about 10-20 miles wide, depending on the extent of the Nile's annual flooding. Even in the green Sahara phase, most of Egypt isn't actually wet enough for agriculture based on rainfall alone. You still need a second source of water, which is either the Nile or one of the lakes that are scattered across Egypt at this time.

Unfortunately, the arrival of agriculture also marks the beginning of the end of Egypt's wet phase. Around 7,000 years ago, the Sahara begins the gradual process of drying as the monsoon retreats southwards again. This process is slow and spread over several thousand years, from around 7,000 to 4,000 years ago. Since the monsoon is retreating southwards, the northern parts are lost to the desert first while southern Egypt is still green.

Here's a chart that shows the archaeology of ancient Egypt overlaid on geographical and temporal scales. The x-axis is time, beginning at 9,000 BC and ending at 1,000 BC. The y-axis is latitude, with north on top. The main geographical areas of Egypt are listed north to south in the first column on the left. The color background shows brown for desert and green for vegetation. Note that everything is brown (desert) before about 9,000 BC. Note also the end of the wet phase on the right, as the greens fade out and brown reappears, but along a north-south curve, with southern parts remaining green (wet) longer.

So, getting back to your question about the pyramids. The answer is that they were built when Egypt was already a desert, but not quite so dry as today. As I mentioned earlier, the drying of the Sahara was a slow process between 7,000 to 4,000 years ago. But around 4,000 years ago things suddenly speeded up, and it became bone dry in just a couple hundred years.

The earliest pyramids date to around 4,600 years ago. This was the tail end of the slow drying phase (when most of Egypt had already lost its grasslands and turned back to desert), but before the accelerated drying phase which began about 4,000 years ago. All the major settlements in the grasslands west of the Nile had already been abandoned thousands of years before the pyramids were built. You can see this in the second chart I linked, where no dots appear in the brown part of the chart at the end of the green phase. Ignore the settlements in the Abu Ballas region for now, they aren't actually settlements, they were waystations set up along a trade route. Nobody lived there permanently.

While most of the desertification had already happened by the time the pyramids were built (in fact, desertification may have been a cause for the rise of Egyptian civilization, as the scattered farmers felt the need to organize to engineer irrigation projects to deal with the spread of the desert), there is evidence that some desertification continued well into the Old Kingdom. The habitable band along the Nile continued to contract for a while, which we can tell from the fact that some of the older monuments appear to have been built too close to the edge of the desert and then abandoned. Possibly when they were built the desert was farther from the Nile, but as it drew closer the buildings had to be abandoned.

Here's some further reading if you're interested:

• Kuper, R., & Kropelin, S. (2006). Climate-Controlled Holocene Occupation in the Sahara : Motor of Africa’s Evolution. Science, 313(August), 803–807.

• Bronk Ramsey, C., Dee, M. W., Rowland, J. M., Higham, T. F. G., Harris, S. a, Brock, F., … Shortland, A. J. (2010). Radiocarbon-based chronology for dynastic Egypt. Science (New York, N.Y.), 328(5985), 1554–1557.