Choose the correct statement for the pair of equations 9x − 3y + 6 = 0 and 3x − y + 2 = 0.
Answer and explanation
Correct answer: There are infinitely many solutions
Write the equations as a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0. Here, a₁/a₂ = 9/3 = 3, b₁/b₂ = (−3)/(−1) = 3, and c₁/c₂ = 6/2 = 3. Since all three ratios are equal, both equations represent the same, or coincident, line. Every point on that line satisfies both equations, so the pair has infinitely many solutions. Options A and D describe different conditions.
Frequently asked questions
What is the correct answer to this question?
There are infinitely many solutions
Why is this the correct answer?
Write the equations as a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0. Here, a₁/a₂ = 9/3 = 3, b₁/b₂ = (−3)/(−1) = 3, and c₁/c₂ = 6/2 = 3. Since all three ratios are equal, both equations represent the same, or coincident, line. Every point on that line satisfies both equations, so the pair has infinitely many solutions. Options A and D describe different conditions.
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.
