What type of pair is formed by the equations (24x+36y=168) and (2x+3y=14)?
Answer and explanation
Correct answer: Consistent and dependent
A pair of linear equations is dependent when both equations represent exactly the same line. Such a pair is consistent because it has solutions, but it does not have just one solution; every point on the common line satisfies both equations. To identify this situation, compare all corresponding coefficients and constants after multiplying or dividing an equation by a non-zero number.
Here, multiplying the second equation by \(12\) gives \(12(2x+3y=14)\), or \(24x+36y=168\). This is exactly the first equation. Therefore, the two equations are the same equation and their graphs coincide. They have infinitely many common solutions, so the pair is consistent and dependent. Choice A is correct; “independent” would mean that the lines meet at only one point.
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What is the correct answer to this question?
Consistent and dependent
Why is this the correct answer?
A pair of linear equations is dependent when both equations represent exactly the same line. Such a pair is consistent because it has solutions, but it does not have just one solution; every point on the common line satisfies both equations. To identify this situation, compare all corresponding coefficients and constants after multiplying or dividing an equation by a non-zero number.
Here, multiplying the second equation by \(12\) gives \(12(2x+3y=14)\), or \(24x+36y=168\). This is exactly the first equation. Therefore, the two equations are the same equation and their graphs coincide. They have infinitely many common solutions, so the pair is consistent and dependent. Choice A is correct; “independent” would mean that the lines meet at only one point.
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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