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

The weight of 7 apples and 12 bananas is gm, and that of 12 apples and 10 bananas is gm. Determine the weight of 4 apples and 9 bananas, given that they are identical.

• Agm
• Bgm
• Cgm
• Dgm

### Example

The weight of 7 apples and 12 bananas is gm, and that of 12 apples and 10 bananas is gm. Determine the weight of 4 apples and 9 bananas, given that they are identical.

### Solution

Let the weight of one apple be denoted by , and the weight of one banana be denoted by . Then, from the information in the question, we can conclude that

This pair of equations can be solved by using the omitting method. Multiplying the first equation by 5 gives

Multiplying the second equation by 6 gives

Subtracting the two equations gives

Substituting this value for into the first equation gives

Therefore, the weight of one apple is and the weight of one banana is .

The weight of 4 apples and 9 bananas is therefore

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