KCET · Maths · Determinants
The system of equations \(x + 2y = 3\) and \(2x + 3y = 3\) has
- A No solution
- B Unique solution
- C Infinite solutions
- D Only two solutions
Answer & Solution
Correct Answer
(B) Unique solution
Step-by-step Solution
Detailed explanation
The given system of equations is:
\(x + 2y = 3\)
\(2x + 3y = 3\)
Comparing with the standard form \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\), we have:
\(\dfrac{a_1}{a_2} = \dfrac{1}{2}\)
\(\dfrac{b_1}{b_2} = \dfrac{2}{3}\)
Since \(\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}\), the lines intersect at a single point.
Therefore, the system of equations has a unique solution.
Answer: Unique solution
\(x + 2y = 3\)
\(2x + 3y = 3\)
Comparing with the standard form \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\), we have:
\(\dfrac{a_1}{a_2} = \dfrac{1}{2}\)
\(\dfrac{b_1}{b_2} = \dfrac{2}{3}\)
Since \(\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}\), the lines intersect at a single point.
Therefore, the system of equations has a unique solution.
Answer: Unique solution
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