Solve {6x + 6y = 13, xy = 1}.

6x + 6y = 13

xy = 1

6y = 13 - 6x

y = (13 - 6x) / 6

x(13 - 6x) / 6 = 1

6x² - 13x + 6 = 0

(2x - 3)(3x - 2) = 0

x = 3 / 2; 2 / 3

y = {13 - 6(3 / 2)} / 6; {13 - 6(2 / 3)} / 6

y = 2 / 3; 3 / 2

solutions as (2 / 3, 3 / 2) and (3 / 2, 2 / 3)

6x + 6y = 13 and xy = 1 cutting each other at (2 / 3, 3 / 2) and (3 / 2, 2 / 3)

 

Solve {10x + 10y = 29, xy = 1}.

10x + 10y = 29

xy = 1

10y = 29 - 10x

y = (29 - 10x) / 10

x(29 - 10x) / 10 = 1

10x² - 29x + 10 = 0

(2x - 5)(5x - 2) = 0

x = 5 / 2; 2 / 5

y = {29 - 10(5 / 2)} / 10; {29 - 10(2 / 5)} / 10

y = 2 / 5; 5 / 2

solutions as (2 / 5, 5 / 2) and (5 / 2, 2 / 5)

10x + 10y = 29 and xy = 1 cutting each other at (2 / 5, 5 / 2) and (5 / 2, 2 / 5)

 

Solve {15x + 15y = 34, xy = 1}.

15x + 15y = 34

xy = 1

15y = 34 - 15x

y = (34 - 15x) / 15

x(34 - 15x) / 15 = 1

15x² - 34x + 15 = 0

(3x - 5)(5x - 3) = 0

x = 5 / 3; 3 / 5

y = {34 - 15(5 / 3)} / 15; {34 - 15(3 / 5)} / 15

y = 3 / 5; 5 / 3

solutions as (3 / 5, 5 / 3) and (5 / 3, 3 / 5)

15x + 15y = 34 and xy = 1 cutting each other at (3 / 5, 5 / 3) and (5 / 3, 3 / 5)