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

Our 28^{th} 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 Arithmetic**, *p. 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