How many solutions will the equations (8x+3y=19) and (16x+6y=45) have?
Answer and explanation
Correct answer: No solution
Compare the ratios of the corresponding coefficients: \(8/16=3/6=1/2\), whereas the ratio of the constant terms is \(19/45\), which is not \(1/2\). Thus, the two lines are parallel and distinct, so they have no common point and the pair has no solution. Infinitely many solutions would require all three ratios to be equal. 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?
Compare the ratios of the corresponding coefficients: \(8/16=3/6=1/2\), whereas the ratio of the constant terms is \(19/45\), which is not \(1/2\). Thus, the two lines are parallel and distinct, so they have no common point and the pair has no solution. Infinitely many solutions would require all three ratios to be equal. 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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