Question

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

Answer 1

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

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

Since x and y are integers

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

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

Therefore, if we take

$7x+2y=11$

$4x+y=1$

Then solving these two linear equations we get

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

If we take

$7x+2y=-11$

$4x+y=-1$

Then solving these two linear equations we get

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

If we take

$7x+2y=1$

$4x+y=11$

Then solving these two linear equations we get

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

If we take

$7x+2y=-1$

$4x+y=-11$

Then solving these two linear equations we get

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

Thus the ordered pairs will be

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

Total number of ordered pairs = 4

Hope this answer is helpful.

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Answer 2

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