For (2x+3y=13) and (4x+6y=26), what is the relation among (a_1/a_2), (b_1/b_2), and the constant ratio?
Answer and explanation
Correct answer: All three ratios are equal
Here, a₁/a₂ = 2/4 = 1/2, b₁/b₂ = 3/6 = 1/2, and the ratio of the constants is 13/26 = 1/2. Hence, all three ratios are equal. This means that both equations represent the same line, so the pair has infinitely many solutions. Exam tip: When a₁/a₂ = b₁/b₂ = c₁/c₂, the two lines are coincident and the pair has infinitely many solutions.
Frequently asked questions
What is the correct answer to this question?
All three ratios are equal
Why is this the correct answer?
Here, a₁/a₂ = 2/4 = 1/2, b₁/b₂ = 3/6 = 1/2, and the ratio of the constants is 13/26 = 1/2. Hence, all three ratios are equal. This means that both equations represent the same line, so the pair has infinitely many solutions. Exam tip: When a₁/a₂ = b₁/b₂ = c₁/c₂, the two lines are coincident and the pair has infinitely many 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.
