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Mathematics · Pair of Linear Equations in Two Variables · NCERT Examples

Example 10

A complete, independently verified solution for NCERT Example 10.

Mathematics · Chapter 3 · NCERT Examples

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NCERT Example

Example 10

elimination method · digits problem

A two-digit number plus its reversal is 66. Its digits differ by 2. Find all such numbers.

Solution

Let x and y be the tens and units digits.

(10x+y)+(10y+x)=66⇒x+y=6(10x+y)+(10y+x)=66\Rightarrow x+y=6
x−y=2⇒(x,y)=(4,2)x-y=2\Rightarrow(x,y)=(4,2)
y−x=2⇒(x,y)=(2,4)y-x=2\Rightarrow(x,y)=(2,4)

Both numbers sum with their reversals to 66.

Final answer

The numbers are 42 and 24.