How many solutions will the pair (10x+3y=17) and (20x+9y=31) have?
Answer and explanation
Correct answer: One unique solution
For the two equations, the coefficient ratios are \(\frac{10}{20}=\frac{1}{2}\) and \(\frac{3}{9}=\frac{1}{3}\), which are unequal. Hence, the lines are not parallel and intersect at exactly one point. Therefore, the pair has one unique solution. In the no-solution case, the first two ratios are equal but the ratio of constants is different. Exam tip: first compare \(\frac{a_1}{a_2}\) and \(\frac{b_1}{b_2}\).
Frequently asked questions
What is the correct answer to this question?
One unique solution
Why is this the correct answer?
For the two equations, the coefficient ratios are \(\frac{10}{20}=\frac{1}{2}\) and \(\frac{3}{9}=\frac{1}{3}\), which are unequal. Hence, the lines are not parallel and intersect at exactly one point. Therefore, the pair has one unique solution. In the no-solution case, the first two ratios are equal but the ratio of constants is different. Exam tip: first compare \(\frac{a_1}{a_2}\) and \(\frac{b_1}{b_2}\).
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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