Which statement is correct for (13x+2y=19) and (4x+5y=11)?
Answer and explanation
Correct answer: Lines intersect at one point
Write the equations in the standard form a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0. Their coefficient ratios are a₁/a₂=13/4 and b₁/b₂=2/5. These values are unequal, so the two lines do not have proportional coefficients and cannot be parallel or coincident. Equivalently, their slopes are -13/2 and -4/5, which are different. Two non-parallel lines in a plane intersect at exactly one point, so the pair is consistent and independent and has one unique solution. Thus option C is correct; options A, B, and D incorrectly describe parallel or coincident cases.
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What is the correct answer to this question?
Lines intersect at one point
Why is this the correct answer?
Write the equations in the standard form a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0. Their coefficient ratios are a₁/a₂=13/4 and b₁/b₂=2/5. These values are unequal, so the two lines do not have proportional coefficients and cannot be parallel or coincident. Equivalently, their slopes are -13/2 and -4/5, which are different. Two non-parallel lines in a plane intersect at exactly one point, so the pair is consistent and independent and has one unique solution. Thus option C is correct; options A, B, and D incorrectly describe parallel or coincident cases.
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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