1. **State the problem:** Solve the simultaneous equations: $$y - 2x = 10$$ $$2x + 5y = 26$$ 2. **Rewrite the first equation to express $y$ in terms of $x$: ** $$y = 2x + 10$$ 3. **Substitute $y = 2x + 10$ into the second equation:** $$2x + 5(2x + 10) = 26$$ 4. **Expand and simplify:** $$2x + 10x + 50 = 26$$ $$12x + 50 = 26$$ 5. **Isolate $x$ by subtracting 50 from both sides:** $$12x + \cancel{50} - \cancel{50} = 26 - 50$$ $$12x = -24$$ 6. **Divide both sides by 12 to solve for $x$:** $$\frac{12x}{\cancel{12}} = \frac{-24}{\cancel{12}}$$ $$x = -2$$ 7. **Substitute $x = -2$ back into $y = 2x + 10$ to find $y$:** $$y = 2(-2) + 10 = -4 + 10 = 6$$ 8. **Final solution:** $$\boxed{(x, y) = (-2, 6)}$$ This is the point where the red and green lines intersect on the graph, confirming the solution to the simultaneous equations.