Solve System 270B4F

1. **State the problem:** Solve the system of equations: $$7x - y = 7$$ $$x + 2y = 6$$ 2. **Choose a method:** We will use substitution or elimination. Here, let's use substitution. 3. **Isolate $y$ in the first equation:** $$7x - y = 7 \implies y = 7x - 7$$ 4. **Substitute $y$ into the second equation:** $$x + 2(7x - 7) = 6$$ 5. **Simplify and solve for $x$:** $$x + 14x - 14 = 6$$ $$15x - 14 = 6$$ $$15x = 6 + 14$$ $$15x = 20$$ $$x = \frac{20}{15}$$ $$x = \frac{\cancel{20}}{\cancel{15}} = \frac{4}{3} = 1 \frac{1}{3}$$ 6. **Substitute $x$ back to find $y$:** $$y = 7\left(\frac{4}{3}\right) - 7 = \frac{28}{3} - 7 = \frac{28}{3} - \frac{21}{3} = \frac{7}{3} = 2 \frac{1}{3}$$ 7. **Final solution:** $$x = 1 \frac{1}{3}, \quad y = 2 \frac{1}{3}$$ 8. **Match with choices:** This corresponds to choice D. **Answer:** D $x = 1 \frac{1}{3}$, $y = 2 \frac{1}{3}$