Sophia and paisley go to the movie theater and purchase refreshments for their friends. sophia spends a total of $32.75 on 3 bags of popcorn and 5 drinks. paisley spends a total of $51.25 on 6 bags of popcorn and 7 drinks.

the price of a drink is $4.8

Step-by-step explanation:

Let x represent the price of a bag of popcorn.

Let y represent the price of one drink.

Sophia spends a total of $32.75 on 3 bags of popcorn and 5 drinks. This means that

3x + 5y = 32.75 - - - - - - - - - -1

Paisley spends a total of $51.25 on 6 bags of popcorn and 7 drinks. This means that

6x + 7y = 51.25 - - - - - - - - - - - -2

Multiplying equation 1 by 2 and equation 2 by 1, it becomes

6x + 10y = 65.5

6x + 7y = 51.25

Subtracting, it becomes

3y = 14.25

y = 14.25/3 = 4.75

Substituting y = 4.75 into equation 1, it becomes

3x + 5 × 4.75 = 32.75

3x + 23.75 = 32.75

3x = 32.75 - 23.75 = 9

x = 9/3 = 3

{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

600,000,000,000, or 6e14

step-by-step explanation: