If w, x, y, and z are real numbers satisfying:
w+x+y = -2
w+x+z = -4
w+y+z = 19
x+y+z = 12,
what is wx + yz?
+128474 w+x+y = -2
w+x+z = -4
w+y+z = 19
x+y+z = 12
subtract the second equation from the first ⇒ y - z = 2 ⇒ z = y - 2
subtract the third equation from the second ⇒ x - y = -23 ⇒ x = y - 23
x + y + z = 12
(y -23) + y + ( y -2) = 12
3y -25 = 12
3y = 37
y = 37/3
z = y -2 = 37/3 -2 = 31/3
x = t -23 = 37/3 - 23 = -32/3
w + x + z = -4
w - 32/3 + 31/3 = -4
w - 1/3 = -4
w = - 4 + 1/3 = -11/3
wx + yz =
(-11/3) ( -32/3) + ( 37/3) (31/3) = 1499 / 9
