1. We are given two straight lines: $$3x + y = 1$$ $$x + 2y = 7$$ We need to find their point of intersection, which means finding values of $x$ and $y$ that satisfy both equations simultaneously. 2. Express $y$ from the first equation: $$3x + y = 1 \\ y = 1 - 3x$$ 3. Substitute $y = 1 - 3x$ into the second equation: $$x + 2(1 - 3x) = 7$$ 4. Simplify and solve for $x$: $$x + 2 - 6x = 7 \\ -5x + 2 = 7 \\ -5x = 7 - 2 \\ -5x = 5 \\ x = \frac{5}{-5} = -1$$ 5. Substitute $x = -1$ back into the expression for $y$: $$y = 1 - 3(-1) = 1 + 3 = 4$$ 6. The point of intersection of the two lines is: $$\boxed{(-1, 4)}$$