KCET 2026 Mathematics Solved Paper

Concept:For two linear equations in two variables, if $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$, then the lines intersect at exactly one point, giving a unique solution.Explanation:Write the given equations in standard form $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$.First equation: $x + 2y = 3$ becomes $x + 2y - 3 = 0$.So, $a_1 = 1$, $b_1 = 2$, $c_1 = -3$.Second equation: $2x + 3y = 3$ becomes $2x + 3y - 3 = 0$.So, $a_2 = 2$, $b_2 = 3$, $c_2 = -3$.Now compare the ratios:$\frac{a_1}{a_2} = \frac{1}{2}$ and $\frac{b_1}{b_2} = \frac{2}{3}$.Since $\frac{1}{2} \neq \frac{2}{3}$, the lines are not parallel and intersect at exactly one point.Hence, the system of equations has a unique solution.Answer:Option B: Unique solution.