Which equation is obtained by simplifying (6x+3y=12)?
Answer and explanation
Correct answer: (2x+y=4)
The governing concept is preserving an equation while reducing it to an equivalent simpler form. Every term on both sides must be divided by the same non-zero common factor. In 6x + 3y = 12, the common factor is 3. Dividing each term by 3 gives 6x/3 + 3y/3 = 12/3, hence 2x + y = 4. Therefore option B is correct. Option A divides the coefficients but leaves the constant 12 unchanged, option C changes the coefficient of x incorrectly, and option D leaves the original y coefficient and constant. The simplified equation has exactly the same solutions as the original because the same non-zero operation was applied to both sides.
Frequently asked questions
What is the correct answer to this question?
(2x+y=4)
Why is this the correct answer?
The governing concept is preserving an equation while reducing it to an equivalent simpler form. Every term on both sides must be divided by the same non-zero common factor. In 6x + 3y = 12, the common factor is 3. Dividing each term by 3 gives 6x/3 + 3y/3 = 12/3, hence 2x + y = 4. Therefore option B is correct. Option A divides the coefficients but leaves the constant 12 unchanged, option C changes the coefficient of x incorrectly, and option D leaves the original y coefficient and constant. The simplified equation has exactly the same solutions as the original because the same non-zero operation was applied to both sides.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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