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Mathematics

Form the pair of linear equations for the following problem and find their solution by substitution method.

The difference between two numbers is 26 and one number is three times the other. Find them.

Linear Equations

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Answer

Let first number be x, second number be y and x > y.

Given,

Difference between two numbers is 26.

∴ x - y = 26 ……..(1)

Also,

One number is three times the other.

∴ x = 3y …………(2)

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

⇒ 3y - y = 26

⇒ 2y = 26

⇒ y = 262\dfrac{26}{2} = 13.

Substituting value of y in equation (2), we get :

⇒ x = 3 × 13 = 39.

Hence, pair of linear equations are x - y = 26 and x = 3y, where x and y are two numbers such that x > y; x = 39 and y = 13.

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