1. **State the problem:** We are given two linear equations: $$4y = 4 - 2x$$ and $$x + 5y = -7$$ We want to find the point where these two lines intersect. 2. **Rewrite each equation in slope-intercept form $y = mx + b$:** From the first equation: $$4y = 4 - 2x$$ Divide both sides by 4: $$y = \frac{4 - 2x}{4}$$ $$y = \frac{4}{4} - \frac{2x}{4}$$ $$y = 1 - 0.5x$$ From the second equation: $$x + 5y = -7$$ Subtract $x$ from both sides: $$5y = -7 - x$$ Divide both sides by 5: $$y = \frac{-7 - x}{5}$$ $$y = -\frac{7}{5} - \frac{x}{5}$$ 3. **Set the two expressions for $y$ equal to find $x$:** $$1 - 0.5x = -\frac{7}{5} - \frac{x}{5}$$ 4. **Solve for $x$:** Multiply both sides by 10 to clear denominators: $$10(1 - 0.5x) = 10\left(-\frac{7}{5} - \frac{x}{5}\right)$$ $$10 - 5x = -14 - 2x$$ Add $5x$ to both sides: $$10 = -14 + 3x$$ Add 14 to both sides: $$24 = 3x$$ Divide both sides by 3: $$x = \frac{24}{3}$$ $$x = 8$$ 5. **Substitute $x=8$ back into one of the original equations to find $y$:** Using $y = 1 - 0.5x$: $$y = 1 - 0.5(8)$$ $$y = 1 - 4$$ $$y = -3$$ **Final answer:** The lines intersect at the point $$\boxed{(8, -3)}$$.