If (\frac{a_1}{a_2}\neq\frac{b_1}{b_2}), what is the conclusion for a pair of two linear equations?
Answer and explanation
Correct answer: Unique solution
A pair of linear equations in two variables represents two lines. If the ratios of the coefficients of x and y are unequal, the lines do not have the same slope. Lines with different slopes meet at exactly one point, so the pair has one and only one ordered pair satisfying both equations. This is called a unique solution, which is option C.
The condition is \(a_1/a_2\ne b_1/b_2\). Because the coefficient ratios differ, the lines cannot be parallel or coincident. The constants may affect the exact location of the intersection, but they do not change this conclusion when the two coefficient ratios are unequal. Therefore, “no solution” and “infinitely many solutions” are not suitable choices here. The correct conclusion is an unique, or अद्वितीय, solution.
Frequently asked questions
What is the correct answer to this question?
Unique solution
Why is this the correct answer?
A pair of linear equations in two variables represents two lines. If the ratios of the coefficients of x and y are unequal, the lines do not have the same slope. Lines with different slopes meet at exactly one point, so the pair has one and only one ordered pair satisfying both equations. This is called a unique solution, which is option C.
The condition is \(a_1/a_2\ne b_1/b_2\). Because the coefficient ratios differ, the lines cannot be parallel or coincident. The constants may affect the exact location of the intersection, but they do not change this conclusion when the two coefficient ratios are unequal. Therefore, “no solution” and “infinitely many solutions” are not suitable choices here. The correct conclusion is an unique, or अद्वितीय, solution.
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.
