Directions (6-10): In the following questions, two equations numbered ...
6.
I. x^2 + 15x + 56 = 0
(x+7)(x+8)=0
x=-7, -8
II. y^2 -23y + 132 = 0
(y-11)(y-12)=0
y=11, 12
From the given options, the only common solution is (x=-8, y=12). Hence, option D is correct.
7.
I. x^2 - 5x - 6 = 0
(x-6)(x+1)=0
x=6, -1
II. y^2 + 11y + 18 = 0
(y+2)(y+9)=0
y=-2, -9
From the given options, the only common solution is (x=-1, y=-9). Hence, option B is correct.
8.
I. x^2 - 2x - 15 = 0
(x-5)(x+3)=0
x=5, -3
II. y^2 - 6y + 8 = 0
(y-4)(y-2)=0
y=4, 2
From the given options, the only common solution is (x=5, y=2). Hence, option A is correct.
9.
I. x^2 - 6x + 8 = 0
(x-4)(x-2)=0
x=4, 2
II. y^2 - 5y + 6 = 0
(y-2)(y-3)=0
y=2, 3
From the given options, the only common solution is (x=2, y=2). Hence, option C is correct.
10.
I. x^2 - 10x + 16 = 0
(x-8)(x-2)=0
x=8, 2
II. y^2 - 18y + 77 = 0
(y-11)(y-7)=0
y=11, 7
From the given options, the only common solution is (x=2, y=11). Hence, option B is correct.