KCET · Maths · Matrices
The system of equations \(4 x+6 y=5\) and \(8 x+12 y=10\) has
- A No solution
- B Infinitely many solutions
- C A unique solution
- D Only two solutions
Answer & Solution
Correct Answer
(B) Infinitely many solutions
Step-by-step Solution
Detailed explanation
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
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
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