1. **State the problem:** Solve the system of equations using the elimination method: $$7x - 5y = 26$$ $$2x + x = 5$$ 2. **Simplify the second equation:** $$2x + x = 3x = 5$$ 3. **Express $x$ from the second equation:** $$x = \frac{5}{3}$$ 4. **Substitute $x = \frac{5}{3}$ into the first equation:** $$7\left(\frac{5}{3}\right) - 5y = 26$$ 5. **Simplify the substitution:** $$\frac{35}{3} - 5y = 26$$ 6. **Isolate $y$:** $$-5y = 26 - \frac{35}{3}$$ Convert 26 to fraction with denominator 3: $$26 = \frac{78}{3}$$ So, $$-5y = \frac{78}{3} - \frac{35}{3} = \frac{43}{3}$$ 7. **Divide both sides by $-5$ to solve for $y$:** $$y = \frac{\cancel{\frac{43}{3}}}{\cancel{-5}} = -\frac{43}{15}$$ 8. **Final solution:** $$x = \frac{5}{3}, \quad y = -\frac{43}{15}$$