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What is Vedic Astrology?
Vedic Astrology or Jyotish is the system of astrology that was developed by the ancient sages of India, and has been practiced for more than 5,000 years now. It is a part of the Vedic knowledge, which includes the sciences of Ayurveda, Yoga and Vastu to name a few. Vedic Astrology developed through thousands of years of these sages correlating astronomical observation with the movements of earthly life. It is used as a tool for self-examination and understanding, as well as for living harmoniously and consciously with the various energies at play in the universe. Vedic Astrology, or Jyotish, as it is called in Sanskrit, is meant to be used as a means of transcending the energies that bind us to material existence and suffering.

What is the Difference between Vedic Astrology ( Jyotish ) and Western Astrology?
Western Astrology has its roots in the Vedic Astrological tradition. However, much of what Europeans learned from Asia and the Middle East about astrology was buried or completely lost during the Dark Ages and Inquisition. Astrology, like herbalism, alchemy, and magic, was looked upon as anti-Christian, and its practitioners were persecuted. Hence, with the return to European progress, astrology has re-emerged, but has forged a path of its own. One of the essential differences between the two systems is that in Vedic Astrology, the position of the planets is described by astronomically correct observation. Both an Astronomer and a Vedic Astrologer would agree that when the Moon is in Taurus, it can be observed in the night sky, positioned in the actual constellation of Taurus. The zodiac used in Vedic Astrology coincides with the observable constellations. Western Astrology employs a zodiac that is loosely related to the actual constellations, but the position of the planets is determined by a static concept that generates the positional information. If a Western Astrologer were to join an Astronomer and a Vedic Astrologer on a starry night when the Moon was located in Taurus, he would look at his ephemeris (a chart of planetary positions) and say, "Well, it says right here that the Moon is in Gemini." This is the essential difference.

What do you mean by 'A systematic approach'?
Systematic way means that the remedies would work as suggested by the horoscope itself. As an example, if Sun is found in your second house being the lord of the fifth house, doing a remedy to Sun would cause changes in your life regarding your finance, children, diet, creativity and other areas of life ruled by houses second and fifth. It will not affect any other fields of life that Sun is not connected with, in your chart.