1. **State the problem:** Solve the system of linear equations using substitution: $$4x + 3y = 26$$ $$y = 3x - 13$$ 2. **Substitute** the expression for $y$ from the second equation into the first equation: $$4x + 3(3x - 13) = 26$$ 3. **Simplify** the equation: $$4x + 9x - 39 = 26$$ $$13x - 39 = 26$$ 4. **Solve for** $x$: $$13x = 26 + 39$$ $$13x = 65$$ $$x = \frac{65}{13} = 5$$ 5. **Find** $y$ by substituting $x=5$ into $y = 3x - 13$: $$y = 3(5) - 13 = 15 - 13 = 2$$ 6. **Final solution:** $$x = 5, \quad y = 2$$ This means the two lines intersect at the point $(5, 2)$.