What is the correct description of the graph of (2x+11y=27) and (5x+19y=46)?
Answer and explanation
Correct answer: Lines intersecting at one point
For the two equations, \,\(a_1/a_2=2/5\) and \,\(b_1/b_2=11/19\). Since \,\(2/5 \ne 11/19\), the two lines have different slopes and intersect at exactly one point. Hence, the pair has a unique solution. Distinct parallel lines require \,\(a_1/a_2=b_1/b_2\), which is not true here. Exam tip: first compare \,\(a_1/a_2\) and \,\(b_1/b_2\).
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What is the correct answer to this question?
Lines intersecting at one point
Why is this the correct answer?
For the two equations, \,\(a_1/a_2=2/5\) and \,\(b_1/b_2=11/19\). Since \,\(2/5 \ne 11/19\), the two lines have different slopes and intersect at exactly one point. Hence, the pair has a unique solution. Distinct parallel lines require \,\(a_1/a_2=b_1/b_2\), which is not true here. Exam tip: first compare \,\(a_1/a_2\) and \,\(b_1/b_2\).
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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