Find the point of intersection of the lines r | vedclass

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(C) Let the given equation be $f(x, y) = 2x^2 + 3xy + y^2 - 7x - 5y + 6 = 0$. To find the point of intersection $(h, k)$,we take partial derivatives w

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$(1, 1)$

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(C) Let the given equation be $f(x, y) = 2x^2 + 3xy + y^2 - 7x - 5y + 6 = 0$. To find the point of intersection $(h, k)$,we take partial derivatives with respect to $x$ and $y$ and set them to zero. $\frac{\partial f}{\partial x} = 4x + 3y - 7 = 0$ (Equation $1$) $\frac{\partial f}{\partial y} = 3x + 2y - 5 = 0$ (Equation $2$) Multiply Equation $1$ by $2$ and Equation $2$ by $3$: $8x + 6y - 14 = 0$ $9x + 6y - 15 = 0$ Subtracting the first from the second: $(9x - 8x) + (6y - 6y) - (15 - 14) = 0 \implies x - 1 = 0 \implies x = 1$. Substitute $x = 1$ into Equation $1$: $4(1) + 3y - 7 = 0 \implies 3y - 3 = 0 \implies y = 1$. Thus,the point of intersection is $(1, 1)$.

Find the point of intersection of the lines represented by the curve $2x^2 + 3xy + y^2 - 7x - 5y + 6 = 0$.

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