xy = 8
x + y = 6
x + y = 6
x - x + y = -x + 6
y = -x + 6
xy = 8
x(-x + 6) = 8
x(-x) + x(6) = 8
-x² + 6x = 8
-x² + 6x - 8 = 0
-1(x²) - 1(-6x) - 1(8) = 0
-1(x² - 6x + 8) = 0
-1 -1
x² - 6x + 8 = 0
x² - 4x - 2x + 8 = 0
x(x) - x(4) - 2(x) + 2(4) = 0
x(x - 4) - 2(x - 4) = 0
(x - 2)(x - 4) = 0
x - 2 = 0 or x - 4 = 0
+ 2 + 2 + 4 + 4
x = 2 or x = 4
x + y = 6
2 + y = 6
- 2 - 2
y = 4
(x, y) = (2, 4)
or
x + y = 6
4 + y = 6
- 4 - 4
y = 2
(x, y) = (4, 2)
The two numbers that add up to 6 and multiply to 8 are 4 and 2.
