1. **Stating the problem:** Solve the system of linear equations given by: $$1x + 6y = 372$$ $$6ux + 12y = 780$$ with the coordinate pair $(18, 59)$ provided as a potential solution. 2. **Understanding the problem:** We want to verify if $(x, y) = (18, 59)$ satisfies the equations and find the value of $u$ in the second equation. 3. **Substitute $x=18$ and $y=59$ into the first equation:** $$1(18) + 6(59) = 18 + 354 = 372$$ This matches the right side, so the first equation is satisfied. 4. **Substitute $x=18$ and $y=59$ into the second equation:** $$6u(18) + 12(59) = 780$$ Simplify: $$108u + 708 = 780$$ 5. **Solve for $u$:** $$108u = 780 - 708$$ $$108u = 72$$ $$u = \frac{72}{108}$$ Show cancellation: $$u = \frac{\cancel{72}^{\times 12}}{\cancel{108}^{\times 12}} = \frac{6}{9} = \frac{2}{3}$$ 6. **Final answer:** $$u = \frac{2}{3}$$ The coordinate pair $(18, 59)$ satisfies the first equation and determines $u = \frac{2}{3}$ in the second equation.