# MSC #28: By Addition and By Subtraction: Solving a system of equations:

“The equations of two lines are x + y = 14, and x − y = 2 . What are the coordinates of the point of intersection? A (4, 10); B (10, 4); C (7, 7); D (6, 8); E (8,6). “

This question, given in the intermediate level of the 1^{st} International Vedic Mathematics Olympiad, is a variation of the common problem given in elementary school math competitions: “The sum of two numbers is **A** while their difference is **B. **Find the two numbers.”

This is easily solved using the Sutra “By Addition and By Subtraction”, which is the technique
discussed in the 28^{th} of our 30 MATH-Inic Specials for Christmas series.

*Algebra Made Easy as Arithmetic**,*p. 53.

*Addition and subtraction of the two equations will result to having the coefficients of the x and x terms numerically equal. This will enable us to reduce both the sum and difference to (x + y) and (x-y) forms. Then we will apply “by addition and by subtraction again: I. 8x – 3y = 22 II. 3x – 8y = – 33 III. 11x – 11y = – 11; by addition I + II; IV. x – y = – 1; simplify equation III V. 5x + 5y = 55; by Subtraction I – II VI. x + y = 11; simplify equation V VII. 2x = 10; x = 5; by addition IV + VI VIII. 2y = 12; y = 6; by subtraction VI – IV*