Which option is correct for (x+3y=7) and (2x+5y=9)?
Answer and explanation
Correct answer: One unique solution
For the first equation, a₁=1 and b₁=3, while for the second equation, a₂=2 and b₂=5. Here, \(a₁/a₂=1/2\) and \(b₁/b₂=3/5\), so the ratios are unequal. Therefore, the two lines intersect at one point and the pair has a unique solution. In fact, the solution is \(x=-8, y=5\). Exam tip: If \(a₁/a₂ \ne b₁/b₂\), a pair of linear equations has a unique solution.
Frequently asked questions
What is the correct answer to this question?
One unique solution
Why is this the correct answer?
For the first equation, a₁=1 and b₁=3, while for the second equation, a₂=2 and b₂=5. Here, \(a₁/a₂=1/2\) and \(b₁/b₂=3/5\), so the ratios are unequal. Therefore, the two lines intersect at one point and the pair has a unique solution. In fact, the solution is \(x=-8, y=5\). Exam tip: If \(a₁/a₂ \ne b₁/b₂\), a pair of linear equations has a unique 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.
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