Can you help me solve (picture above) A) x = 6, m< LMN = 138°
B) x = 3, m< LMN = 27°
C) x = 3, m< LMN = 24°
D) x = 6, m< LMN = 111°

Step-by-step explanation:

∠LMO = ∠NMO

15x - 21 = x + 63

15x - x = 63 + 21

14x = 84

x = 84/14

x = 6

∠LMN = ∠LMO + ∠NMO

∠LMN = 15x - 21 + x + 63

∠LMN = 15(6) - 21 + 6 + 63

∠LMN = 138°

{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