Sankalana - Vyavakalanabhyam:

*By addition and by subtraction*
Sankalana - Vyavakalanabhyam is the seventh

sutra of

Vedic mathematics. Its corollary is

Yavadunam Tavadunikritya Varga Yojayet.

This sutra, like

Anurupye - Shunyamanyat, is used for solving simultaneous equations. This sutra is used when the

coefficient are interchanged. I'll give an example:

Solve for y and z in the following equations in which y and z remain

constant:

69y - 5z = 42

5y - 69z = 32

Notice that the y-coefficients and the z-coefficients (69 and 5) are interchanged.

There are three steps by which this sutra can be used to solve for y and z:

**Step One: Addition:**
(69y - 5z)

**+** (5y - 69z) = 42

**+** 32

This can be simplified to 74y - 74z = 74

Now divide 70 by 74 to simplify the equation to

**y - z = 1** This will be used in the next step.

**Step Two: Subtraction:**
(69y - 5z)

**-** (5y - 69z) = 42

**-** 32

Simply this to 56y - -56z = 10

56y + 56z = 10

**y + z = 5/28**
**Step Three: We can now use these two equations from steps one and two to solve for y and z**
y = 1 + z = 5/28 - z

1 + z = 5/28 - z

1 + 2z = 5/28

2z = -23/28

z = (-23/28)/2

**z = -23/56**
Therefore, y = 5/28 - -23/56

y = 10/56 + 23/56

**y = 33/56**
To see more examples of this sutra, view the resources below:

**RESOURCES:**

*Vedic Mathematics* by Sri Bharati Krisna Tirthaji

http://www.vedamu.org/Mathematics/course.asp

http://www.sanalnair.org/articles/vedmath/intro.htm

http://www.vedicganita.org/ganitsutras.htm

http://hinduism.about.com/library/weekly/aa062901a.htm

http://www.vedicmaths.org/

http://www.hinduism.co.za/vedic.htm

*Mathemagics* by Arthur Benjamin and Michael B. Shermer

http://en.wikipedia.org/wiki/Vedic_math

http://www.tifr.res.in/~vahia/dani-vmsm.pdf

http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html