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

Our 28^{th} 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”