If (x=2y) and (x+y=9), what is the value of (x)?
Answer and explanation
Correct answer: x=6
The governing method is substitution: use the expression given for one variable in the other equation. Since x=2y, replace x in x+y=9 by 2y. This gives 2y+y=9, so 3y=9 and y=3. Substituting this value back into x=2y gives x=2(3)=6. Therefore option B is correct. A direct check confirms the pair (x,y)=(6,3): it satisfies x=2y because 6=2×3, and it satisfies x+y=9 because 6+3=9. Option A is the value of y rather than x, option C merely repeats the total x+y, and option D results from an incorrect multiplication or addition. The substitution method is appropriate because one equation already expresses x directly in terms of y.
Frequently asked questions
What is the correct answer to this question?
x=6
Why is this the correct answer?
The governing method is substitution: use the expression given for one variable in the other equation. Since x=2y, replace x in x+y=9 by 2y. This gives 2y+y=9, so 3y=9 and y=3. Substituting this value back into x=2y gives x=2(3)=6. Therefore option B is correct. A direct check confirms the pair (x,y)=(6,3): it satisfies x=2y because 6=2×3, and it satisfies x+y=9 because 6+3=9. Option A is the value of y rather than x, option C merely repeats the total x+y, and option D results from an incorrect multiplication or addition. The substitution method is appropriate because one equation already expresses x directly in terms of y.
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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