For two numbers, the equations (5x+2y=31) and (2x-3y=4) are formed. What will be the solution status?
Answer and explanation
Correct answer: One unique solution
For the given equations, \(a_1=5, b_1=2\) and \(a_2=2, b_2=-3\). Since \(\frac{a_1}{a_2}=\frac{5}{2}\) is not equal to \(\frac{b_1}{b_2}=\frac{2}{-3}\), the two lines intersect at exactly one point. Hence, the pair has one unique solution. No solution or infinitely many solutions can occur only when these two ratios are equal. Exam tip: compare \(\frac{a_1}{a_2}\) and \(\frac{b_1}{b_2}\) first.
Frequently asked questions
What is the correct answer to this question?
One unique solution
Why is this the correct answer?
For the given equations, \(a_1=5, b_1=2\) and \(a_2=2, b_2=-3\). Since \(\frac{a_1}{a_2}=\frac{5}{2}\) is not equal to \(\frac{b_1}{b_2}=\frac{2}{-3}\), the two lines intersect at exactly one point. Hence, the pair has one unique solution. No solution or infinitely many solutions can occur only when these two ratios are equal. Exam tip: compare \(\frac{a_1}{a_2}\) and \(\frac{b_1}{b_2}\) first.
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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