How many solutions will (9x-4y=17) and (18x-8y=39) have?
Answer and explanation
Correct answer: No solution
For the two equations, \(\frac{a_1}{a_2}=\frac{9}{18}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{-4}{-8}=\frac{1}{2}\), but \(\frac{c_1}{c_2}=\frac{17}{39}\neq\frac{1}{2}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), so the lines are parallel and distinct and the pair has no solution. Exam tip: this ratio condition identifies inconsistent equations with zero solutions.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
For the two equations, \(\frac{a_1}{a_2}=\frac{9}{18}=\frac{1}{2}\) and \(\frac{b_1}{b_2}=\frac{-4}{-8}=\frac{1}{2}\), but \(\frac{c_1}{c_2}=\frac{17}{39}\neq\frac{1}{2}\). Thus, \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\), so the lines are parallel and distinct and the pair has no solution. Exam tip: this ratio condition identifies inconsistent equations with zero solutions.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
