# 9.6.1. Solving Two First-Degree Equations Algebraically and Geometrically

Determine the two-digit number whose sum of digits is 9, and when the two digits are reversed, the resulting number is more than the original one by 27.

• A36
• B63
• C69
• D96

### Example

Determine the two-digit number whose sum of digits is 9, and when the two digits are reversed, the resulting number is more than the original one by 27.

### Solution

Denote the first digit of the number by and the second digit by . If the sum of the digits is 9, then

Using place value, the value of the number is . If the digits are reversed, the value of the new number will be .

If the reversed number is 27 more than the original number, then which can be rearranged to

Dividing by 9 gives

The pair of simultaneous equations can be solved using the omitting method. Adding the two equations together eliminates the variable and gives

Substituting this value of into the original equation gives

Therefore, the two digit number is 36.

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