What is the correct solution status for (17x+6y=52) and (8x+3y=25)?
Answer and explanation
Correct answer: One unique solution
For two linear equations, a unique solution exists when \\(a_1/a_2 \\ne b_1/b_2\\). Here, \\(17/8 \\ne 6/3\\); equivalently, the determinant is \\(17 \\times 3 - 8 \\times 6 = 3 \\ne 0\\). Therefore, the two lines intersect at exactly one point, so the system has one unique solution. Exam tip: Compare corresponding coefficients in the same order in both equations.
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What is the correct answer to this question?
One unique solution
Why is this the correct answer?
For two linear equations, a unique solution exists when \\(a_1/a_2 \\ne b_1/b_2\\). Here, \\(17/8 \\ne 6/3\\); equivalently, the determinant is \\(17 \\times 3 - 8 \\times 6 = 3 \\ne 0\\). Therefore, the two lines intersect at exactly one point, so the system has one unique solution. Exam tip: Compare corresponding coefficients in the same order in both equations.
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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