Find the fixed point through which the line x | vedclass

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(C) The given equation is $x(a + 2b) + y(a + 3b) = a + b$.Rearranging the terms to group $a$ and $b$:$x(a + 2b) + y(a + 3b) - (a + b) = 0$$ax + 2bx +

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$(2, -1)$

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(C) The given equation is $x(a + 2b) + y(a + 3b) = a + b$.Rearranging the terms to group $a$ and $b$:$x(a + 2b) + y(a + 3b) - (a + b) = 0$$ax + 2bx + ay + 3by - a - b = 0$$a(x + y - 1) + b(2x + 3y - 1) = 0$For this equation to hold for all values of $a$ and $b$,the coefficients of $a$ and $b$ must be zero independently:$x + y - 1 = 0 \implies x + y = 1$ $(i)$$2x + 3y - 1 = 0 \implies 2x + 3y = 1$ $(ii)$Multiplying equation $(i)$ by $2$,we get $2x + 2y = 2$ $(iii)$.Subtracting $(iii)$ from $(ii)$:$(2x + 3y) - (2x + 2y) = 1 - 2$$y = -1$Substituting $y = -1$ into equation $(i)$:$x - 1 = 1 \implies x = 2$Thus,the fixed point is $(2, -1)$.

Find the fixed point through which the line $x(a + 2b) + y(a + 3b) = a + b$ always passes for all values of $a$ and $b$.

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