Poi Algebra 22E0F4

1. **State the problem:** Find the point of intersection (POI) of the system of equations: $$\text{(1) } x + 2y = 4$$ $$\text{(2) } 3x + 2y = 8$$ 2. **Solve for $x$ and $y$ using algebra:** From equation (1), solve for $x$: $$x = 4 - 2y$$ 3. **Substitute $x$ into equation (2):** $$3(4 - 2y) + 2y = 8$$ 4. **Simplify and solve for $y$:** $$12 - 6y + 2y = 8$$ $$12 - 4y = 8$$ Subtract 12 from both sides: $$\cancel{12} - 4y = 8 - \cancel{12}$$ $$-4y = -4$$ Divide both sides by $-4$: $$\frac{-4y}{-4} = \frac{-4}{-4}$$ $$y = 1$$ 5. **Substitute $y=1$ back into equation (1) to find $x$:** $$x + 2(1) = 4$$ $$x + 2 = 4$$ Subtract 2 from both sides: $$x = 4 - 2$$ $$x = 2$$ 6. **Check the solution $(x,y) = (2,1)$ in both equations:** Equation (1): $$2 + 2(1) = 2 + 2 = 4$$ (True) Equation (2): $$3(2) + 2(1) = 6 + 2 = 8$$ (True) 7. **Conclusion:** The point of intersection (POI) is at $$\boxed{(2,1)}$$. 8. **Regarding POI locations:** - The POI is at $(2,1)$ which is in the first quadrant (top-right), not top-left or bottom-right.