Gina, Sam, and Robby all chose movies they would like to see over the next year. They each chose some dramas, comedies, and documentaries. Gina chose 11 movies total. Sam chose twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He chose 27 movies total. Robby chose 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina. Which system of equations represents their movie choices?

x + y + z = 11

2x + 2y + 3z = 27

x + 2y + 2z = 19

x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

x + y + z = 11

2x + 3y + 2z = 27

2x + 3y + 3z = 19

x + y + z = 11

3x + 2y + 2z = 27

x + 2y + 2z = 19

 x+y+z=11

               2x+3y+2z=27

                x+2y+2z=19

Step-by-step explanation:

Let dramas be x, comedies be y and documentaries be z.

Gina chose 11 movies total which will be kept on one side of the is equal to sign. It is not specified how many dramas, comedies and documentaries she chose so we denote it by x, y and z respectively. The sum of x, y and z make up a total of 11 so we have the following equation:

x+y+z=11

Sam's choice of movies are compared to Gina's. He chose twice as many dramas as Gina and we represented dramas by x so we have 2 multiplied by x written as 2x. He chose 3 times as many comedies as Gina so we have 3 multiplied by x which is equal to 3x. Finally he chose twice as many documentaries as Gina and Gina chose z so we have 3 multiplied by z which is equal to 3z. He chose a total of 27 movies which will be equal to the sum of the individual movies we evaluated earlier. So we have the following equation.

2x+3y+2z=27

Robby's choice is also compared to Gina's. He chose the same number of dramas as Gina which was x. He chose twice as many comedies as Gina so 2 multiplied by y is equal to 2y. Finally he chose twice as many documentaries as Gina. 2 multiplied by z is 2z. He chose a total of 19 movies and the sum of the drama, comedy and documentary movies gives us the following equation.

x+2y+2z=19  

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.