Linear Equations - Integral Solutions

Very Important

We are given only one or two equations, but constraints are there on variables such as the solutions must be integers, positive integers etc.

Eg. ax + by = c

Step 1: Find any single integer solution by trial and error. Let the solution be (x0, y0)

Step 2: For every b units x increases, y must decrease by a units (or vice-versa).

Step 3: Check the constraints

Question 1

What is the total number of natural number solutions to 3X+2Y = 50 if X < Y?

Question 2

A carrot, costing Rs. 30, has 50 units of Vitamin A and a beetroot, costing Rs. 40, has 60 units of Vitamin A. How should Ram spend Rs. 1200 to gain the maximum amount of Vitamin A?

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Linear Equations - Integral Solutions

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Solving Linear Equations - 2 Variables

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