Question

Number of non- negative integral solution for the equation 2x + 3y =12 is ​

Answer 1

Step-by-step explanation:

(x;y)=(3;2)

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Answer 2

One thing to remember is that non-negative means all numbers that are not negative. Therefore, 0 and other positive numbers together are known as non-negative numbers. Positive also means that all positive integers, i.e. all integers greater than 0.

In mathematics, integers are the collection of whole numbers and negative numbers. Like whole numbers, whole numbers do not include a fractional part. So we can say that whole numbers are numbers that can be positive, negative, or zero but cannot be a fraction. Examples of integers are 1, 2, 5,8, -9, -12, etc. The symbol for integers is "Z".

According to the question we have

$2x+3y=12$

We can also write it as

$y=\frac{12-2x}{3}$

For y to be an integer we have to find a value such that 12-2x must be a multiple of 3.

So a number that is nonnegative and also multiple of 3, x must be 0,3,4.

Hence the total number of non-negative solutions of the given equation is 3.

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