 # MSC #28 – By Addition and By Subtraction: Solving a System of Linear Equations

Our 28th Math 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 Arithmeticp. 53.

Addition and subtraction of two such 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 can apply “by addition and by subtraction again:

This is illustrated in our featured example as:

I.   5x – 2y = 14

II. 2x – 5y = – 7

By addition (I + II) →7x – 7y = 7; x – y = 1 (III)

By Subtraction (I – II) → V. 3x + 3 = 21; x + y =7 (IV)

By Addition (III + IV) → 2x = 8; x = 4

By Subtraction (IV – III) → 27y = 6; y = 3

We can then check our answers by substituting the values we obtained for x and y in the given equations:

5(4) – 2(3) = 20 – 6 = 14

2(4) – 5(3) = 8 – 15 = -7