Question

The equation of the straight line which passes through the intersection of the lines $x-y-1=0$ and $2x-3y+1=0$ and is parallel to x-axis, is

• A. $y=3$
• B. $y=-3$
• C. $x+y=3$
• D. None of these

Hint:

The equation of the straight line which passes through the intersection of the lines $x-y-1=0$ and $2x-3y+1=0$ and is parallel to x-axis, is

Answer 1

The Correct Option is A

Step 1: Concept
A line passing through the intersection of two lines $L_{1}, L_{2}$ is $L_{1} + \lambda L_{2} = 0$.
Step 2: Analysis
$(x-y-1) + \lambda(2x-3y+1) = 0 \Rightarrow (2\lambda+1)x - (3\lambda+1)y + (\lambda-1) = 0$.
Step 3: Evaluation
For the line to be parallel to the x-axis, the coefficient of $x$ must be zero. Thus, $2\lambda+1 = 0 \Rightarrow \lambda = -1/2$.
Step 4: Conclusion
Substituting $\lambda = -1/2$ back into the equation yields $y=3$.
Final Answer: (a)