# MSC #28- By Addition and By Subtraction: Solving simultaneous equations.

Our 28th MATH-Inic Special for Christmas is the use of the Sutra ”By Addition and By Subtraction” in solving simultaneous linear equations. Using this Sutra, we can easily eliminate a variable. This is especially handy in cases where the coefficients of the X and Y variables are interchanged as can be seen in our example for today which was taken from our book 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 to each other.  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

More examples will be discussed in Chapter 28 of “30 Master Strategies in Computing”