If 6x + 2y = 28 and 3x + y = 14, which statement is correct?
Answer and explanation
Correct answer: The first equation is 2 times the second
The governing idea is equivalence of equations and the effect of multiplying every term by the same non-zero number. Starting with 3x + y = 14, multiply the left side and the right side by 2: 2(3x + y) = 2(14). This becomes 6x + 2y = 28, which is exactly the first equation. Therefore the first equation is twice the second, so both equations represent the same line and do not produce two different independent equations. Option A states this accurately. Option B is false because equivalent equations do not necessarily give different solutions. Options C and D are false because x is present and both equations have constants.
Frequently asked questions
What is the correct answer to this question?
The first equation is 2 times the second
Why is this the correct answer?
The governing idea is equivalence of equations and the effect of multiplying every term by the same non-zero number. Starting with 3x + y = 14, multiply the left side and the right side by 2: 2(3x + y) = 2(14). This becomes 6x + 2y = 28, which is exactly the first equation. Therefore the first equation is twice the second, so both equations represent the same line and do not produce two different independent equations. Option A states this accurately. Option B is false because equivalent equations do not necessarily give different solutions. Options C and D are false because x is present and both equations have constants.
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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