For two numbers, the equations (6x+5y=49) and (3x-2y=7) are formed. What will be the solution status?
Answer and explanation
Correct answer: One unique solution
For the given equations, a₁/a₂ = 6/3 = 2 and b₁/b₂ = 5/(-2) = -5/2. Since a₁/a₂ ≠ b₁/b₂, the two lines intersect at exactly one point, so the pair has a unique solution. Infinitely many solutions would require a₁/a₂ = b₁/b₂ = c₁/c₂, which is not true here. Exam tip: first compare the ratios of the coefficients of x and y.
Frequently asked questions
What is the correct answer to this question?
One unique solution
Why is this the correct answer?
For the given equations, a₁/a₂ = 6/3 = 2 and b₁/b₂ = 5/(-2) = -5/2. Since a₁/a₂ ≠ b₁/b₂, the two lines intersect at exactly one point, so the pair has a unique solution. Infinitely many solutions would require a₁/a₂ = b₁/b₂ = c₁/c₂, which is not true here. Exam tip: first compare the ratios of the coefficients of x and y.
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.
