Question

The difference between two integers is 2. The larger integer is 6 less than twice the smaller. Find the integer.




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Answer 1

$\sf\large\green{\underline {given : - }}$

• Difference between two integers is 2.
• Larger integer is 6 less than twice the smaller.

$\\ \sf\large\green{\underline {to \: consider : - }}$

• Let the larger integer be 'x' and smaller integer be 'y'.

$\\ \sf\large\green{\underline { solution : - }}$

Since difference between two integers is 2.

$\sf\large\green{\underline { }}so.. \\ \sf\large\red{x - y = 2 } \: \: \: - - - - (1)$

Larger integer is 6 less than twice the smaller number..

$\sf\large\green{\underline { }}so.. \\ \\ \sf\large\red{ x = 2y - 6} \: \: \: \: \\\sf\large\red {x - 2y = - 6 } \: \: \: \: - - - (2)$

Substracting equation (2) from equation (1) , we get....

$\sf\large\blue {y = 8 }$

Putting this value in equation (1) we get...

$\sf\large\green{\underline { }}x - 8 = 2 \\ \\ \sf\large\blue{ x = 10}$

$\\ \sf\large\green{\underline { verification : - }}$

• We will check by putting the values of the integer in equation (2).

$\sf\large\green{\underline { }}x = 2y - 6 \\ \\ \sf\large\green{\underline { }}10 = 2(8) - 6 \\ \\ \sf\large\green{\underline { }}10 = 16 - 6 \\ \\ \sf\large\green{\underline { }}10 = 10............\sf\large\red { verified}$