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Mathematics

Statement 1: The sum of two numbers x and y is 11. Twice the first number plus three times the second number equals to 25.

⇒ x + y = 11 and 2x + 3y = 25

Statement 2: The numbers are 7 and 4.

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Linear Equations

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Answer

Given, The sum of two numbers x and y is 11.

⇒ x + y = 11

⇒ x = 11 - y ………………..(1)

Twice the first number plus three times the second number equals to 25.

⇒ 2x + 3y = 25 ………(2)

So, statement 1 is true.

Substituting the value of x from equation (1) in (2), we get :

⇒ 2(11 - y) + 3y = 25

⇒ 22 - 2y + 3y = 25

⇒ 22 + y = 25

⇒ y = 25 - 22

⇒ y = 3.

Substitute the value of y in equation (1), we get

⇒ x = 11 - 3 = 8

The numbers are 8 and 3.

So, statement 2 is false.

∴ Statement 1 is true, and statement 2 is false.

Hence, option 3 is the correct option.

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