Find the number of ordered pairs of integers (x, y) such that (2x + y) (5x + 3y) = 7
Answers
Simplifying
(2x + y)(5x + 3y) = 7
Multiply (2x + y) * (5x + 3y)
(2x * (5x + 3y) + y(5x + 3y)) = 7
((5x * 2x + 3y * 2x) + y(5x + 3y)) = 7
Reorder the terms:
((6xy + 10x2) + y(5x + 3y)) = 7
((6xy + 10x2) + y(5x + 3y)) = 7
(6xy + 10x2 + (5x * y + 3y * y)) = 7
(6xy + 10x2 + (5xy + 3y2)) = 7
Reorder the terms:
(6xy + 5xy + 10x2 + 3y2) = 7
Combine like terms: 6xy + 5xy = 11xy
(11xy + 10x2 + 3y2) = 7
Solving
11xy + 10x2 + 3y2 = 7
Solving for variable 'x'.
Reorder the terms:
-7 + 11xy + 10x2 + 3y2 = 7 + -7
Combine like terms: 7 + -7 = 0
-7 + 11xy + 10x2 + 3y2 = 0
there are no integral solution
Answer:
Simplifying
(2x + y)(5x + 3y) = 7
Multiply (2x + y) * (5x + 3y)
(2x * (5x + 3y) + y(5x + 3y)) = 7
((5x * 2x + 3y * 2x) + y(5x + 3y)) = 7
Reorder the terms:
((6xy + 10x2) + y(5x + 3y)) = 7
((6xy + 10x2) + y(5x + 3y)) = 7
(6xy + 10x2 + (5x * y + 3y * y)) = 7
(6xy + 10x2 + (5xy + 3y2)) = 7
Reorder the terms:
(6xy + 5xy + 10x2 + 3y2) = 7
Combine like terms: 6xy + 5xy = 11xy
(11xy + 10x2 + 3y2) = 7
Solving
11xy + 10x2 + 3y2 = 7
Solving for variable 'x'.
Reorder the terms:
-7 + 11xy + 10x2 + 3y2 = 7 + -7
Combine like terms: 7 + -7 = 0
-7 + 11xy + 10x2 + 3y2 = 0
there are no integral solution