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)
Correct Answer: Option A
Explanation
2x + y = 4……(i)
x^2 + xy = -12……..(ii)
from eqn (i), y = 4 – 2x
= x2 + x(4 – 2x)
= -12
x2 + 4x – 2×2 = -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)