1. **State the problem:** We are given two linear equations: $$2x + y = 7$$ $$x - y = 1$$ We need to rearrange each into the slope-intercept form $y = mx + c$ and then find their intersection point. 2. **Rearrange the first equation:** Start with: $$2x + y = 7$$ Subtract $2x$ from both sides: $$y = 7 - 2x$$ 3. **Rearrange the second equation:** Start with: $$x - y = 1$$ Subtract $x$ from both sides: $$-y = 1 - x$$ Multiply both sides by $-1$ to solve for $y$: $$y = \cancel{-1} \times (1 - x) = -1 + x$$ So, $$y = x - 1$$ 4. **Find the intersection point:** Set the two expressions for $y$ equal: $$7 - 2x = x - 1$$ Add $2x$ to both sides: $$7 = 3x - 1$$ Add $1$ to both sides: $$7 + 1 = 3x$$ $$8 = 3x$$ Divide both sides by $3$: $$x = \frac{8}{3}$$ 5. **Find $y$ coordinate:** Substitute $x = \frac{8}{3}$ into $y = x - 1$: $$y = \frac{8}{3} - 1 = \frac{8}{3} - \frac{3}{3} = \frac{5}{3}$$ 6. **Final answer:** The intersection point is: $$\left( \frac{8}{3}, \frac{5}{3} \right)$$