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(B) Step $1$: Find the point of intersection of $x - y + 1 = 0$ $(i)$ and $2x + 3y - 8 = 0$ (ii).From $(i)$, $y = x + 1$. Substitute this into (ii): $

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$x + y - 3 = 0$

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(B) Step $1$: Find the point of intersection of $x - y + 1 = 0$ $(i)$ and $2x + 3y - 8 = 0$ (ii).From $(i)$, $y = x + 1$. Substitute this into (ii): $2x + 3(x + 1) - 8 = 0 \implies 2x + 3x + 3 - 8 = 0 \implies 5x = 5 \implies x = 1$.Then $y = 1 + 1 = 2$. The point of intersection is $(1, 2)$.Step $2$: The line has an $x$-intercept of $3$, so it passes through $(3, 0)$.Step $3$: Find the equation of the line passing through $(1, 2)$ and $(3, 0)$.The slope $m = \frac{0 - 2}{3 - 1} = \frac{-2}{2} = -1$.Using point-slope form $y - y_1 = m(x - x_1)$: $y - 0 = -1(x - 3) \implies y = -x + 3 \implies x + y - 3 = 0$.

The equation of a line passing through the point of intersection of the lines $x - y + 1 = 0$ and $2x + 3y - 8 = 0$ and having an $x$-intercept of $3$ is:

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