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Elena and Koran are playing a board game. After one round, Elena says, “You earned so many more points than I did. If you earned 5 more points, your score would me twice mine!”

Kiran says, “Oh, I don’t think I did that much better. I only scored 9 points higher than you did.”

Write a system of equations to represent each student’s comment. Be sure to specify what your variables represent.

Respuesta :

The system of equations to represent each student comment is:

2x - y = 5

x - y = -9

Solution:

Let "x" be the score point of Elena

Let "y" be the score point of Koran

Elena says, “You earned so many more points than I did

If you earned 5 more points, your score would me twice mine

Which means,

Koran score + 5 = twice of Elena

y + 5 = 2x

Rearranging it we get,

2x - y = 5 ------- eqn 1

Kiran says, “Oh, I don’t think I did that much better

I only scored 9 points higher than you did

Elena score + 9 = Koran score

x + 9 = y

Rearranging it we get,

x - y = -9 --------- eqn 2

Thus eqn 1 and eqn 2 represents eacch student comment

fichoh

The system of equations which represents the scenario described based on the statements made by kiran and Elena are :

  • 2x - y = 5 - - - - - - (1)
  • x - y = - 9 - - - - - (2)

Representing their scores using variables :

  • Elena's score = x
  • Kiran's score = y

Using Elena's statement :

Kiran's score + 5 = Elena's score × 2

y + 5 = 2x

2x - y = 5 - - - - - - (1)

Using Kiran's statement :

y = x + 9

x - y = - 9 - - - - - (2)

Hence, the system of equation is (1) and (2)

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