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in Linear Equations by (34.1k points)
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Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.

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Best answer

Let the greater number be x and the smaller number be y.

According to the first condition, x – y = 3 …(i)

According to the second condition,

3x + 2y = 19 …(ii) 

Multiplying equation (i) by 2, we get

2x – 2y = 6 …(iii)

Adding equations (ii) and (iii), we get

Substituting x = 5 in equation (i), we get

5 – y = 3 

∴ 5 – 3 = y 

∴ y = 2 

∴ The required numbers are 5 and 2.

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