Exercise 6

What does the equation \(y = 3\) represent in \(\mathbb{R}^3\)? What does \(z = 5\) represent? What does the pair of equations \(y = 3, z = 5\) represent? In other words, describe the set of points \((x, y, z)\) such that \(y = 3\) and \(z = 5\). Illustrate with a sketch.