1. The problem involves understanding the equations $x = y + z$ and $f(x) = a^2 + b^2 = c^2$. 2. The first equation $x = y + z$ is a simple linear relation where $x$ is the sum of $y$ and $z$. 3. The second equation $a^2 + b^2 = c^2$ is the Pythagorean theorem, which relates the sides of a right triangle: $a$ and $b$ are the legs, and $c$ is the hypotenuse. 4. To analyze or graph these, we can consider $f(x)$ as a function representing the sum of squares of $a$ and $b$, equal to $c^2$. 5. This implies that for given $a$ and $b$, $c = \sqrt{a^2 + b^2}$. 6. The first equation can be used to express one variable in terms of the others, for example, $y = x - z$. 7. These equations are fundamental in algebra and geometry, often used in physics and engineering contexts. Final answer: The first equation is a linear sum, and the second is the Pythagorean theorem relating sides of a right triangle.