Which statement is correct for the equations (10x+11y=43) and (20x+21y=84)?
Answer and explanation
Correct answer: There is a unique solution
Here, (10/20) \ne (11/21), since 10/20 = 1/2 while 11/21 has a different value. Therefore, the two lines intersect at exactly one point, so the pair has a unique solution. Option A would apply when the first two ratios are equal but the constant-term ratio is different; option C requires all three ratios to be equal. Exam tip: for two linear equations, a₁/a₂ \ne b₁/b₂ always indicates a unique solution.
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What is the correct answer to this question?
There is a unique solution
Why is this the correct answer?
Here, (10/20) \ne (11/21), since 10/20 = 1/2 while 11/21 has a different value. Therefore, the two lines intersect at exactly one point, so the pair has a unique solution. Option A would apply when the first two ratios are equal but the constant-term ratio is different; option C requires all three ratios to be equal. Exam tip: for two linear equations, a₁/a₂ \ne b₁/b₂ always indicates 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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