Which option is correct for (6x+2y=8) and (3x+y=5)?
Answer and explanation
Correct answer: No solution
Dividing the first equation by 2 gives 3x+y=4, whereas the second equation is 3x+y=5. The ratios of the coefficients of x and y are equal, \(6/3=2/1\), but the ratio of the constant terms is different, \(8/5\ne 2\). Thus, the two lines are parallel and distinct, so the pair has no solution. Infinitely many solutions would require both equations to represent the same line. Exam tip: if \(a_1/a_2=b_1/b_2\ne c_1/c_2\), the pair has no solution.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
Dividing the first equation by 2 gives 3x+y=4, whereas the second equation is 3x+y=5. The ratios of the coefficients of x and y are equal, \(6/3=2/1\), but the ratio of the constant terms is different, \(8/5\ne 2\). Thus, the two lines are parallel and distinct, so the pair has no solution. Infinitely many solutions would require both equations to represent the same line. Exam tip: if \(a_1/a_2=b_1/b_2\ne c_1/c_2\), the pair has 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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