What is found by comparing the ratios of (a) and (b) in the equations (13x+8y=47) and (6x+4y=23)?
Answer and explanation
Correct answer: (13/6 \ne 8/4), so one unique solution
A pair of linear equations has one unique solution when the ratios of the coefficients of x and y are unequal. Geometrically, this means the corresponding lines have different slopes, so they cross at one point. If both variable ratios were equal, the constant ratio would then distinguish coincident lines from distinct parallel lines.
Here, \\(13/6\\) is approximately \\(2.167\\), while \\(8/4=2\\). Therefore \\(13/6\\ne8/4\\). The lines have different slopes and must intersect exactly once. The constant terms do not need further comparison for this classification. Hence the system has one unique solution, and option C is correct.
Frequently asked questions
What is the correct answer to this question?
(13/6 \ne 8/4), so one unique solution
Why is this the correct answer?
A pair of linear equations has one unique solution when the ratios of the coefficients of x and y are unequal. Geometrically, this means the corresponding lines have different slopes, so they cross at one point. If both variable ratios were equal, the constant ratio would then distinguish coincident lines from distinct parallel lines.
Here, \\(13/6\\) is approximately \\(2.167\\), while \\(8/4=2\\). Therefore \\(13/6\\ne8/4\\). The lines have different slopes and must intersect exactly once. The constant terms do not need further comparison for this classification. Hence the system has one unique solution, and option C is correct.
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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