1. **State the problem:** We are given two linear equations: $$y = 2x + 4$$ and $$8x + 5y = 10$$ We need to find the intersection point of these two lines, i.e., the values of $x$ and $y$ that satisfy both equations. 2. **Use substitution method:** Since $y$ is already expressed in terms of $x$ in the first equation, substitute $y = 2x + 4$ into the second equation: $$8x + 5(2x + 4) = 10$$ 3. **Simplify the equation:** $$8x + 10x + 20 = 10$$ $$18x + 20 = 10$$ 4. **Isolate $x$:** $$18x = 10 - 20$$ $$18x = -10$$ 5. **Solve for $x$:** $$x = \frac{-10}{18}$$ Show cancellation: $$x = \frac{\cancel{-10}}{\cancel{18}} = \frac{-5}{9}$$ 6. **Find $y$ by substituting $x$ back into the first equation:** $$y = 2\left(-\frac{5}{9}\right) + 4 = -\frac{10}{9} + 4$$ Convert 4 to fraction with denominator 9: $$4 = \frac{36}{9}$$ So, $$y = -\frac{10}{9} + \frac{36}{9} = \frac{26}{9}$$ 7. **Final answer:** The intersection point is $$\left(-\frac{5}{9}, \frac{26}{9}\right)$$