For two numbers the equations (4x+y=19) and (x-3y=2) are formed. What will be the solution status?
Answer and explanation
Correct answer: One unique solution
The determinant of the coefficients is \\(4(-3)-1(1)=-13\\ne0\\). Therefore, the two lines intersect at exactly one point, so the pair has one unique solution. Option B would apply only when the lines are parallel, with equal ratios of the corresponding coefficients. Exam tip: if \\(a_1b_2-a_2b_1\\ne0\\), a pair of linear equations has a unique solution.
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What is the correct answer to this question?
One unique solution
Why is this the correct answer?
The determinant of the coefficients is \\(4(-3)-1(1)=-13\\ne0\\). Therefore, the two lines intersect at exactly one point, so the pair has one unique solution. Option B would apply only when the lines are parallel, with equal ratios of the corresponding coefficients. Exam tip: if \\(a_1b_2-a_2b_1\\ne0\\), a pair of linear equations has a unique 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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