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Question

(A) The equation of a line passing through the intersection of two lines $L_1: x + y - 2 = 0$ and $L_2: 2x - y + 1 = 0$ is given by $L_1 + \lambda L_2

Vedclass · Accepted Answer

$5x - y = 0$

Vedclass · Answer

(A) The equation of a line passing through the intersection of two lines $L_1: x + y - 2 = 0$ and $L_2: 2x - y + 1 = 0$ is given by $L_1 + \lambda L_2 = 0$.$(x + y - 2) + \lambda(2x - y + 1) = 0$.Since the line passes through the origin $(0, 0)$,we substitute $x = 0$ and $y = 0$ into the equation:$(0 + 0 - 2) + \lambda(0 - 0 + 1) = 0$$-2 + \lambda = 0 \Rightarrow \lambda = 2$.Substituting $\lambda = 2$ back into the equation:$(x + y - 2) + 2(2x - y + 1) = 0$$x + y - 2 + 4x - 2y + 2 = 0$$5x - y = 0$.

Find the equation of the line passing through the point of intersection of the lines $x + y - 2 = 0$ and $2x - y + 1 = 0$ and the origin $(0, 0)$.

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