What relationship exists between 2x − 3y = 4 and 4x − 6y = 8?
Answer and explanation
Correct answer: The second equation is 2 times the first
Compare every term of the two equations. Multiplying the first equation, 2x − 3y = 4, by 2 gives 4x − 6y = 8, which is exactly the second equation. Thus the two equations are equivalent and represent the same straight line, called coincident lines. They do not represent two separate lines; instead, every point on the common line satisfies both equations. Consequently, the pair has infinitely many solutions. Option A correctly states the algebraic relationship. Option C would require proportional x- and y-coefficients but a non-proportional constant, while option D would require unequal coefficient ratios.
Frequently asked questions
What is the correct answer to this question?
The second equation is 2 times the first
Why is this the correct answer?
Compare every term of the two equations. Multiplying the first equation, 2x − 3y = 4, by 2 gives 4x − 6y = 8, which is exactly the second equation. Thus the two equations are equivalent and represent the same straight line, called coincident lines. They do not represent two separate lines; instead, every point on the common line satisfies both equations. Consequently, the pair has infinitely many solutions. Option A correctly states the algebraic relationship. Option C would require proportional x- and y-coefficients but a non-proportional constant, while option D would require unequal coefficient ratios.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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