1. \( \begin{array}{l}y=-\frac{3}{2} x+5 \\ y=-\frac{2}{3} x+5\end{array} \)

These two equations represent linear functions with interesting characteristics. The first line, \(y = -\frac{3}{2}x + 5\), has a steep negative slope, indicating it declines sharply as x increases, while the second line, \(y = -\frac{2}{3}x + 5\), has a more gradual negative slope. Intriguingly, both lines share the same y-intercept at (0, 5). This means they cross the y-axis at the same point but spread apart as x moves away from 0. To find the intersection point of these two lines, we need to set them equal to each other: \(-\frac{3}{2}x + 5 = -\frac{2}{3}x + 5\). Simplifying this will reveal whether they intersect or if they are parallel. As the slopes are different, they will indeed intersect somewhere on the Cartesian plane—just a little peak of where they blend together! Happy solving!