Substitution Method 2B8123

1. **State the problem:** Solve the system of equations using the substitution method: $$x + 2y = 6$$ $$y = 2x + 3$$ 2. **Substitution method formula:** Substitute the expression for $y$ from the second equation into the first equation. 3. **Substitute $y = 2x + 3$ into $x + 2y = 6$: ** $$x + 2(2x + 3) = 6$$ 4. **Simplify the equation:** $$x + 4x + 6 = 6$$ $$5x + 6 = 6$$ 5. **Isolate $x$: ** $$5x + 6 - 6 = 6 - 6$$ $$5x = 0$$ $$\cancel{5}x = \cancel{0}$$ $$x = 0$$ 6. **Find $y$ by substituting $x=0$ into $y = 2x + 3$: ** $$y = 2(0) + 3 = 3$$ 7. **Solution:** The solution to the system is the ordered pair: $$(0, 3)$$ 8. **Check:** Substitute $x=0$ and $y=3$ into the first equation: $$0 + 2(3) = 6$$ $$6 = 6$$ which is true. Therefore, the system has a unique solution $(0, 3)$. **Answer:** A. The solution is $(0, 3)$.