Solve {x + y = 4, 4xy = 15}.
x + y = 4
4xy = 15
y = 4 - x
4x(4 - x) = 15
4x² - 16x + 15 = 0
(2x - 3)(2x - 5) = 0
x = 3 / 2; 5 / 2
y = 4 - (3 / 2); 4 - (5 / 2)
y = 5 / 2; 3 / 2
solutions as (3 / 2, 5 / 2) and (5 / 2, 3 / 2)
x + y = 4 and 4xy = 15 cutting each other at (3 / 2, 5 / 2) and (5 / 2, 3 / 2)
Solve {6x + 6y = 19, 2xy = 5}.
6x + 6y = 19
2xy = 5
6y = 19 - 6x
y = (19 - 6x) / 6
2x(19 - 6x) / 6 = 5
6x² - 19x + 15 = 0
(2x - 3)(3x - 5) = 0
x = 3 / 2; 5 / 3
y = {19 - 6(3 / 2)} / 6; {19 - 6(5 / 3)} / 6
y = 5 / 3; 3 / 2
solutions as (3 / 2, 5 / 3) and (5 / 3, 3 / 2)
6x + 6y = 19 and 2xy = 5 cutting each other at (3 / 2, 5 / 3) and (5 / 3, 3 / 2)
Solve {6x + 6y = 25, 6xy = 25}.
6x + 6y = 25
6xy = 25
6y = 25 - 6x
y = (25 - 6x) / 6
6x(25 - 6x) / 6 = 25
6x² - 25x + 25 = 0
(2x - 5)(3x - 5) = 0
x = 5 / 2; 5 / 3
y = {25 - 6(5 / 2)} / 6; {25 - 6(5 / 3)} / 6
y = 5 / 3; 5 / 2
solutions as (5 / 3, 5 / 2) and (5 / 2, 5 / 3)
6x + 6y = 25 and 6xy = 25 cutting each other at (5 / 3, 5 / 2) and (5 / 2, 5 / 3)
Solve {15x + 15y = 16, 15xy = 4}.
15x + 15y = 16
15xy = 4
15y = 16 - 15x
y = (16 - 15x) / 15
15x(16 - 15x) / 15 = 4
15x² - 16x + 4 = 0
(3x - 2)(5x - 2) = 0
x = 2 / 3; 2 / 5
y = {16 - 15(2 / 3)} / 15; {16 - 15(2 / 5)} / 15
y = 2 / 5; 2 / 3
solutions as (2 / 5, 2 / 3) and (2 / 3, 2 / 5)
15x + 15y = 16 and 15xy = 4 cutting each other at (2 / 5, 2 / 3) and (2 / 3, 2 / 5)
Solve {15x + 15y = 19, 5xy = 2}.
15x + 15y = 19
5xy = 2
15y = 19 - 15x
y = (19 - 15x) / 15
5x(19 - 15x) / 15 = 2
15x² - 19x + 6 = 0
(3x - 2)(5x - 3) = 0
x = 2 / 3; 3 / 5
y = {19 - 15(2 / 3)} / 15; {19 - 15(3 / 5)} / 15
y = 3 / 5; 2 / 3
solutions as (3 / 5, 2 / 3) and (2 / 3, 3 / 5)
15x + 15y = 19 and 5xy = 2 cutting each other at (3 / 5, 2 / 3) and (2 / 3, 3 / 5)
Solve {x + y = 1, 25xy = 6}.
x + y = 1
25xy = 6
y = 1 - x
25x(1 - x) = 6
25x² - 25x + 6 = 0
(5x - 2)(5x - 3) = 0
x = 2 / 5; 3 / 5
y = 1 - (2 / 5); 1 - (3 / 5)
y = 3 / 5; 2 / 5
solutions as (2 / 5, 3 / 5) and (3 / 5, 2 / 5)
x + y = 1 and 25xy = 6 cutting each other at (2 / 5, 3 / 5) and (3 / 5, 2 / 5)
