Question

~~Find the equation of the straight line passing through the point of intersection of the two lines x+2y+3=0 and 3x+4y+7=0 and parallel to the straight line y-x=8

Answer 1

Dear student
$$\begin{gathered} \mathrm{x}+2\mathrm{y}+3=0...\left(1\right) \\ 3\mathrm{x}+4\mathrm{y}+7=0...\left(2\right) \\ \mathrm{On}\mathrm{solving}\mathrm{the}\mathrm{above}\mathrm{equations}\mathrm{we}\mathrm{get} \\ \mathrm{x}=-1\mathrm{and}\mathrm{y}=-1 \\ \mathrm{Point}\mathrm{of}\mathrm{intersection}\mathrm{of}\mathrm{x}+2\mathrm{y}+3=0\mathrm{and}\mathrm{is}\left(-1,-1\right) \\ \mathrm{The}\mathrm{equation}\mathrm{of}\mathrm{line}\mathrm{parallel}\mathrm{to}\mathrm{the}\mathrm{straight}\mathrm{line}\mathrm{y}-\mathrm{x}-8=0\mathrm{is}\mathrm{y}-\mathrm{x}+\mathrm{k}=0 \\ -1+1+\mathrm{k}=0 \\ \Rightarrow \mathrm{k}=0 \\ \therefore \mathrm{the}\mathrm{required}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{straight}\mathrm{line}\mathrm{is}\mathrm{y}-\mathrm{x}=0 \end{gathered}$$

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