Question

find the number of ordered pair of inyegers(x,y) such that (7x+2y)(4x+y)=11​

Answer 1

Explanation:

The number of ordered pairs of integers (x,y) such that (7x+2y) (4x+y)=11 is 4

Step-by-step explanation:

To find the number of ordered pairs of integers (x, y) such that

(7x+2y)(4x+y)=11(7x+2y)(4x+y)=11

Since x and y are integers

Therefore, 7x+2y7x+2y and 4x+y4x+y will also be integers

11 is a prime number which can be written as 11\times 111×1 , (-11)\times (-1)(−11)×(−1) , 1\times 111×11 or (-1)\times (-11)(−1)×(−11)

Therefore, if we take

7x+2y=117x+2y=11

4x+y=14x+y=1

Then solving these two linear equations we get

x = -9, y = 37 (x and y are both integers)

If we take

7x+2y=-117x+2y=−11

4x+y=-14x+y=−1

Then solving these two linear equations we get

x = 9, y = -37 (x and y are both integers)

If we take

7x+2y=17x+2y=1

4x+y=114x+y=11

Then solving these two linear equations we get

x = 21, y = -73 (x and y are both integers)

If we take

7x+2y=-17x+2y=−1

4x+y=-114x+y=−11

Then solving these two linear equations we get

x = -21, y = 73 (x and y are both integers)

Thus the ordered pairs will be

(-9, 37), (9, -37), (21, -73), (-21, 73)(−9,37),(9,−37),(21,−73),(−21,73)

Total number of ordered pairs = 4

Hope this answer is helpful.

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