KEAM 2017 Math Paper

(d) In a consistent, the intersection point of two lines, satisfy the third line.
Consider λ=−1, then given equation become
−x−y‌‌=2
2x−3y‌‌=1
⇒x=−1,y‌‌=−1
Third equation is 3x−2y=−1
Put x=−1,y=−1
∴‌‌−3+2=−1
⇒‌‌−1=−1, true
Consider λ=4, then given equation become
4x−y=2
2x−3y=−4
⇒‌‌y=2,x=1
Third equation is 3x−2y=−1
Put y=2,x=1
∴‌‌3−4=−1
⇒‌‌−1=−1, true
Hence option (d) is correct.