For the family of lines given by the equation | vedclass

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(B) The given equation is $(2 + k)x + (1 + k)y = 5 + 7k$. Rearranging the terms to isolate $k$: $2x + kx + y + ky = 5 + 7k$ $(2x + y - 5) + k(x + y -

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The lines pass through the point $(-2, 9)$.

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(B) The given equation is $(2 + k)x + (1 + k)y = 5 + 7k$. Rearranging the terms to isolate $k$: $2x + kx + y + ky = 5 + 7k$ $(2x + y - 5) + k(x + y - 7) = 0$. This represents a family of lines passing through the intersection of the lines $2x + y - 5 = 0$ and $x + y - 7 = 0$. Solving the system of equations: $2x + y = 5$ $x + y = 7$ Subtracting the second from the first: $(2x + y) - (x + y) = 5 - 7$ $x = -2$. Substituting $x = -2$ into $x + y = 7$: $-2 + y = 7 \implies y = 9$. Thus,all lines pass through the fixed point $(-2, 9)$.

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

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