Question

Form the pair of linear equations for the following problems and find the Solution by substitution method :

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

Answer 1

$\huge{\underline{\underline{\mathrm{\red{Answer-}}}}}$

The numbers are 39 and 13 respectively.

$\huge{\underline{\underline{\mathrm{\red{Explanation-}}}}}$

Let the numbers be x and y, say x > y

Condition (1) : The difference between them is 26.

$\implies$ x - y = 26 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (1)

Condition (2) : One number is three times the other.

$\implies$ x = 3y ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (2)

Put the value of eq (2) in (1),

$\implies$ 3y - y = 26

$\implies$ 2y = 26

$\implies$ y = $\sf{\cancel{\dfrac{26}{2}}}$

$\implies$ $\large{\boxed{\green{\rm{y\:=\:13}}}}$

Now, put the value of y in equation (2),

$\implies$ x = 3 ( 13 )

$\implies$ $\large{\boxed{\green{\rm{x\:=\:39}}}}$

Hence, the numbers are 39 and 13 respectively.

Answer 2

$\huge{\underline{\red{\mathcal{AnsWer}}}}$

Y = 13 and X = 39

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