Question

If x and y are integers, then the equation 7x + 13y = 100 has
​

Answer 1

Given :   x and y are integers,   equation 7x + 13y = 100  

To Find : Number of solutions

Solution:

7x + 13y = 100  

=> 7x  + 14y - y  = 100

=> 7 (x + 2y)  = 7 * 14  + 2 + y

=> 7 ( x + 2y - 14)  =  y + 2

y + 2 must be a multiple of 7

y = 5 ,    

Hence y  = 5

=> x =  5

( 5 , 5) is the only solution considering only positive integers

Other wise infinite solutions

where y is of form     y = 7k - 2 where k is an integere

y = -2    => x =   18  

and x is of form = 13m  + 5   where m is integer

Learn more:

How many ordered pairs of (m,n) integers satisfy m/12=12/m ...

brainly.in/question/13213839

Identify the ordered pairs that result in a quadrilaterala) (1.-1), (2,-2 ...

brainly.in/question/17225822

Answer 2

Answer:

Infinite solution.

Step-by-step explanation:

Given:  x and y are integers & equation is 7x + 13y = 100.

To find : Number of solutions.

In this case, the number of solution are infinite as for every x we can find the corresponding value of y.

7x +13y = 100  

7x +14y - y  = 100

7 (x +2y)  = 7 * 14  + 2 + y

7 ( x + 2y-14)  =  y + 2

In order to get an integer value, y+2 must be a multiple of 7.

y = 7k - 2 where k is an integer

And x is of form = 13m  + 5   where m is an integer.

#SPJ2