xy = 12
x + y = 7
x + y = 7
x - x + y = -x + 7
y = -x + 7
xy = 12
x(-x + 7) = 12
x(-x) + x(7) = 12
-x² + 7x = 12
-x² + 7x - 12 = 0
-1(x²) - 1(-7x) - 1(12) = 0
-1(x² - 7x + 12) = 0
-1 -1
x² - 7x + 12 = 0
x² - 4x - 3x + 12 = 0
x(x) - x(4) - 3(x) -3(-4) = 0
x(x - 4) - 3(x - 4) = 0
(x - 3)(x - 4) = 0
x - 3 = 0 or x - 4 = 0
+ 3 + 3 + 4 + 4
x = 3 x = 4
x + y = 7
3 + y = 7
- 3 - 3
y = 4
(x, y) = (3, 4)
or
x + y = 7
4 + y = 7
- 4 - 4
y = 3
(x, y) = (4, 3)
The two numbers that mutliplies to 12 and add up to 7 are 3 and 4.