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 is A

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)