Which pair of linear equations has one unique solution?
Answer and explanation
Correct answer: 4x + y = 8 and 2x + 3y = 7
The governing concept is that a pair has one unique solution when the two lines intersect, which occurs when a₁/a₂ ≠ b₁/b₂. In option C, the x-coefficient ratio is 4/2 = 2, while the y-coefficient ratio is 1/3; these are unequal, so the lines have different slopes and meet at exactly one point. Therefore option C is correct. In option A, both equations are equivalent, giving infinitely many solutions. In option D, the same dependence occurs because the first equation is five times the second. In option B, the coefficient ratios are equal, but the constant ratios differ, so the lines are distinct parallel lines and there is no solution.
Frequently asked questions
What is the correct answer to this question?
4x + y = 8 and 2x + 3y = 7
Why is this the correct answer?
The governing concept is that a pair has one unique solution when the two lines intersect, which occurs when a₁/a₂ ≠ b₁/b₂. In option C, the x-coefficient ratio is 4/2 = 2, while the y-coefficient ratio is 1/3; these are unequal, so the lines have different slopes and meet at exactly one point. Therefore option C is correct. In option A, both equations are equivalent, giving infinitely many solutions. In option D, the same dependence occurs because the first equation is five times the second. In option B, the coefficient ratios are equal, but the constant ratios differ, so the lines are distinct parallel lines and there is no 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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