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(NONE) Step $1$: Find the point of intersection of the lines $x + 2y + 6 = 0$ and $2x - y = 2$.From the second equation,$y = 2x - 2$.Substitute this i

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$x - y + 5 = 0$

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(NONE) Step $1$: Find the point of intersection of the lines $x + 2y + 6 = 0$ and $2x - y = 2$.From the second equation,$y = 2x - 2$.Substitute this into the first equation: $x + 2(2x - 2) + 6 = 0$.$x + 4x - 4 + 6 = 0 \implies 5x + 2 = 0 \implies x = -\frac{2}{5}$.Then $y = 2(-\frac{2}{5}) - 2 = -\frac{4}{5} - \frac{10}{5} = -\frac{14}{5}$.The point of intersection is $(-\frac{2}{5}, -\frac{14}{5})$.Step $2$: The equation of a line with $y$-intercept $c = 5$ is $y = mx + 5$.Since the line passes through $(-\frac{2}{5}, -\frac{14}{5})$,we have:$-\frac{14}{5} = m(-\frac{2}{5}) + 5$.$-\frac{14}{5} - 5 = -\frac{2}{5}m \implies -\frac{39}{5} = -\frac{2}{5}m \implies m = \frac{39}{2}$.Step $3$: The equation is $y = \frac{39}{2}x + 5 \implies 2y = 39x + 10 \implies 39x - 2y + 10 = 0$.

The equation of the line passing through the point of intersection of the lines $x + 2y + 6 = 0$ and $2x - y = 2$ and making an intercept $5$ on the $y$-axis is

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