Find the line through the meeting point of x + 2y - 5 = 0 and 3x - y - 1 = 0 that also passes…

Step 1. The meeting point. From the second equation $y = 3x - 1$. Then $x + 6x - 2 - 5 = 0$, so $x = 1$ and $y = 2$.

Step 2. Find $k$. At $(0, 1)$: $(2 - 5) + k(-1 - 1) = 0$, so $-3 - 2k = 0$ and $k = -1.5$.

Step 3. The line. $(x + 2y - 5) - 1.5(3x - y - 1) = 0$ gives $-3.5x + 3.5y - 3.5 = 0$, which is $x - y + 1 = 0$.

Step 4. The $y$-intercept. With $x = 0$: $y = 1$.