Cyclic (General) Formula This is a GENERAL formula of Vedic Mathematics which can be applied to any 2 equations for obtaining 2 unknown values. Consider following 2 general equations ax + by = p cx + dy = q Solving, x = (bq – pd) / (bc - ad) y = (cp - aq) / (bc - ad) Notice that for calculation of numerators (x any y) cyclic method is used and Denominators remains same for both x and y. Examples: 2x + 3y =6 3x + 4y = 3 Applying above formula: x = (9 – 24)/ (9 - 8) = -15 y = (18 - 6) (9 - 8) = 12 -3x + 5y = 2 4x + 3y = -5 Applying above formula: x = (-25 -6) / (20+9) = -31/29 y = (8-15) / (20+9) = -7/29 Sunyam Anyat Sanskrit Name: शून्यमन्यत् English Translation: If one is in ratio then other is 0. Prerequisites: Ratio of 1 of the variables should be = ratios of RHS. Meaning: If above condition is satisfied then other variable = 0. The variable which was in ratio = Ratio of RHS and its corresponding coefficient. Examples: 3x + 2y = 4 6x + 3y = 8 Here coefficients of (x) are in ratio 1:2 which is same as that of RHS. So according the Sunyam Anyat, y= 0. And x is calculated by taking the ratio of RHS and coeff i.e. 4/3 or 8/6. Hence x = 4/3. 12x + 8y = 7 16x + 16y = 14 Here coeff of y and RHS are in same ratio. So x = 0 and y = 7/8.   Sankalana Vyavakalanabhyam Sanskrit Name: संकलनव्यवकलनाभ्याम् English Translation: Addition and Subtraction.(Addition and Subtraction gives x+y and x-y expressions). Prerequisites: Coefficient of 1 variable in 1st equation should be same to other in 2nd equation (+/- matterless.) Meaning: If coefficient of 1 variable 1st equation is same as that of other in 2nd equation then Adding and Subtracting both the equations brings equations in the form of ‘x+y’ and ’x-y’ which can be EASILY solved simultaneously. Examples: 2x + 3y = 5 3x + 2y = 6 Adding both Equations gives, 5x + 5y = 11. Hence x + y = 11/5. Subtracting both equation gives, -x + y = -1 Now … [Read more...]