Q94 / 180 · KCET 2025 · Mathematics

The system of equations $4 x+6 y=5$ and $8 x+12 y=10$ has

A
No solution
Correct answer
B
Infinitely many solutions
C
A unique solution
D
Only two solutions

Solution

Given equations: 1. $4 x+6 y=5$ 2. $8 x+12 y=10$ Step-by-step check: Multiply Equation (1) by 2: $2(4 x+6 y)=2(5) \Rightarrow 8 x+12 y=10$ This is same as Equation (2). Conclusion: Both equations represent the same line $\Longrightarrow$ Infinitely many solutions

Hence, the correct answer is option: 'B'.

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