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