# By Addition and By Subtraction

As I was browsing through the questions in yesterday’s **1 ^{st} International Vedic Mathematics Olympiad (IVMO 2021)**, I saw that two questions which appeared in both the Intermediate and Senior Olympiads were exactly among the topics of my online synchronous meeting with my

**AMEA 2021-D**class this morning.

The techniques discussed in **Chapter 18 – By Addition and By Subtraction **and **Chapter 19 – Solving Simultaneous Equations : x and y coefficients interchanged** of my **Algebra Made Easy as Arithmetic** book can be used to solve mentally each of the two Olympiad questions in less that 5 seconds.

The first question was: ** The equations of two lines are x + y = 14 and x – y = 2. What are the coordinates of their point of intersection?**”

This can be solved mentally using the Vedic Math Sutra ** By Addition and By Subtraction**.

**By**

**adding**the two equations we can eliminate the y variable giving 2x = 16 or x = 8.

**By subtracting** the second equation from the first, we can eliminate the x variable and obtain 2y = 12 or y = 6. Therefore, the coordinates of the point of intersection,** (x, y) is (8, 6)**.

Even elementary school learners can solve this problem mentally when expressed in this form: ** The sum of two numbers is 14, while their difference is 2. Find the numbers**.

The second question seems harder to solve: ** If 5x – y = 18 and 5y – x = 12, find the value of (x – y)**.

A closer look at the problem will show that the coefficients of x and y are interchanged in the two equations. We can simply **subtract** the second equation from the first to 6x – 6y = 6 or **(x -y) = 1**.