Question

For the straight lines given by the equation $(2+k)x+(1+k)y=5+7k,$ for different values of k which of the following statements is true

• A. Lines are parallel
• B. Lines pass through the point $(–2,9)$
• C. Lines pass through the point $(2,–9)$
• D. None of these

Answer 1

The correct option is B

Lines pass through the point $(–2,9)$

Explanation for the correct options:

Simplifying the equation we get:

$(2+k)x+(1+k)y=5+7k$

$\Rightarrow 2x+kx+y+ky–7k–5=0$

$\Rightarrow (2x+y–5)+k(x+y–7)=0$

Equating, $2x+y–5=0\dots \left(i\right)$

and $(x+y–7)=0\dots \left(ii\right)$

Solving $\left(i\right)$and $\left(ii\right)$

We get $x=-2$and $y=9$

So the line passes through $(-2,9)$

Hence, Option(B) is correct.