Solve for (x, y) in the equation 2x + y = 4: x^2 + xy = -12
A
(6, -8): (-2, 8)
B
(3, -4): (-1, 4)
C
(8, -4): (-1, 4)
D
(-8, 6): (8, -2)
E
(-4, 3): (4, -1)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
2x + y = 4......(i)
x^2 + xy = -12........(ii)
from eqn (i), y = 4 - 2x
= x2 + x(4 - 2x)
= -12
x2 + 4x - 2x2 = -12
4x - x2 = -12
x2 - 4x - 12 = 0
(x - 6)(x + 2) = 0
sub. for x = 6, in eqn (i) y = -8, 8
=(6,-8); (-2, 8)
Source: Myschool Past Questions Archive (Record #32228)