Hoang has worked as a nurse at Springfield General Hospital for 7 years longer than her friend Bill. Two years ago, she had been at the hospital for twice as long. How long has each been at the hospital

Hoang has been working for 16 years in the hospital, while Bill has been working there for 9 years.

Step-by-step explanation:

Since Hoang has worked as a nurse at Springfield General Hospital for 7 years longer than her friend Bill, and two years ago, she had been at the hospital for twice as long, to determine how long has each been at the hospital must be performed the following mathematical logical reasoning:

-The difference between the two is 7 years

-2 years ago, the difference was the same, but Hoang doubled Bill in the number of years, that is, she had been 14 years in the hospital, and Bill had been 7 yeats in the hospital (2 x 7 = 14).

-So, as of today, Hoang has been working for 16 years in the hospital, while Bill has been working there for 9 years.

{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