Question

If the lines $x+y=|a|$ and $ax-y=1$ intersect in the first quadrant then

• A. a∈ (1, 4)
• B. a∈ (1, ∞)
• C. a∈ (0, 4)
• D. a∈ (0, ∞)

Answer 1

The correct option is B

a∈ (1, ∞)

The intersection point of the lines $y=ax-1$ and $x+y=|a|$ is $(\frac{1+|a|}{1+a},\frac{a|a|-1}{1+a})$

The above point will lie in the first quadrant if $1+a>0$ and $a|a|>1.$
Solving the above inequalities we have $a>1$