What type of pair is formed by the equations (30x+45y=210) and (2x+3y=14)?
Answer and explanation
Correct answer: Consistent and dependent
When one equation in a pair is a non-zero multiple of the other, both equations describe the same line. The pair is then called consistent and dependent. It has infinitely many solutions, because every point on that common line satisfies both equations. A quick test is to multiply the coefficients and the constant term of one equation by the same number and check whether the other equation results exactly.
Multiplying \(2x+3y=14\) by \(15\) gives \(30x+45y=210\), which is precisely the first equation. Thus the two equations are not different lines; they coincide completely. Therefore the pair is consistent and dependent, and choice A is correct. It would be incorrect to call it independent, since independent lines intersect at only one point, while these equations have infinitely many common solutions.
Frequently asked questions
What is the correct answer to this question?
Consistent and dependent
Why is this the correct answer?
When one equation in a pair is a non-zero multiple of the other, both equations describe the same line. The pair is then called consistent and dependent. It has infinitely many solutions, because every point on that common line satisfies both equations. A quick test is to multiply the coefficients and the constant term of one equation by the same number and check whether the other equation results exactly.
Multiplying \(2x+3y=14\) by \(15\) gives \(30x+45y=210\), which is precisely the first equation. Thus the two equations are not different lines; they coincide completely. Therefore the pair is consistent and dependent, and choice A is correct. It would be incorrect to call it independent, since independent lines intersect at only one point, while these equations have infinitely many common solutions.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
