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The Difference of Two Numbers is 3, and the Sum of Three Times the Larger One and Twice the Smaller One is 19. Find the Two Numbers.

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Question

The difference of two numbers is 3, and the sum of three times the larger one and twice the smaller one is 19. Find the two numbers.

Sum
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Solution

Let the larger number be x and the smaller number be y.
According to given information, we have
x - y = 3
⇒ x - 3 + y   ....(i)
Also, 3x + 2y = 19
⇒ 3(3 + y) + 2y = 19    ....[From (i)]
⇒ 9 + 3y + 2y = 19
⇒ 5y = 10
⇒ y = 2
⇒ x = 3 + 2
= 5
Thus, the required numbers are 5 and 2 respectively.

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Methods of Solving Simultaneous Linear Equations by Elimination Method
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Chapter 8: Simultaneous Linear Equations - Exercise 8.3

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Frank Mathematics [English] Class 9 ICSE
Chapter 8 Simultaneous Linear Equations
Exercise 8.3 | Q 2

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