What is the correct conclusion by observing the equations (16x-12y=44) and (4x-3y=12)?
Answer and explanation
Correct answer: No solution
Dividing the first equation by 4 gives \(4x-3y=11\), whereas the second equation is \(4x-3y=12\). The ratios of the coefficients of \(x\) and \(y\) are equal, but the ratio of the constant terms is different: \(16/4=(-12)/(-3)=4\), while \(44/12=11/3\). Hence, the two lines are parallel and distinct, so they have no common solution. Option C would be correct only if all three ratios were equal. Exam tip: if \(a_1/a_2=b_1/b_2\ne c_1/c_2\), the pair of linear equations is inconsistent and 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 4 gives \(4x-3y=11\), whereas the second equation is \(4x-3y=12\). The ratios of the coefficients of \(x\) and \(y\) are equal, but the ratio of the constant terms is different: \(16/4=(-12)/(-3)=4\), while \(44/12=11/3\). Hence, the two lines are parallel and distinct, so they have no common solution. Option C would be correct only if all three ratios were equal. Exam tip: if \(a_1/a_2=b_1/b_2\ne c_1/c_2\), the pair of linear equations is inconsistent and 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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