Factor completely. 2x^2y + 2xy + 4x + 4 a. (2x + 4)(xy + 1) b. (2x + 4y)(x + 1) c. 2(xy + 2)(x + 1) d. (2xy + 4)(x + 1)

2(xy + 2)(x + 1)   (C)

Step-by-step explanation:

2x^2y + 2xy + 4x + 4

= 2xy(x + 1) + 4(x + 1)

= (2xy + 4)(x + 1)

=  2(xy + 2)(x + 1)

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

14

step-by-step explanation: