In the given image, there are two graphs. The question asks to solve the system of equations represented by each graph and write the system of equations.

Part a: Graph Analysis

In the first graph, we can see a parabola and a line intersecting each other.

1. The parabola appears to have its vertex at the origin (0,0), and the general shape suggests it is of the form $y = x^2$.
2. The line crosses the y-axis at $y = -2$ and has a positive slope, possibly of the form $y = 2x - 2$ based on the visual estimate.

System of equations for part a:

$\text{1) } y = x^2$ $\text{2) } y = 2x - 2$ Solution: To find the points of intersection, solve the system by substituting $y = x^2$ into $y = 2x - 2$. $x^2 = 2x - 2$ $x^2 - 2x + 2 = 0$ This is a quadratic equation, and solving this will give the points of intersection.

Part b: Graph Analysis

In the second graph, there is also a parabola and a line.

1. The parabola has a vertex at $(2, 0)$, and it opens upwards, so its equation likely is $y = (x - 2)^2$.
2. The line seems to have a slope of 1 and crosses the y-axis at $y = -2$, indicating its equation is $y = x - 2$.

System of equations for part b:

$\text{1) } y = (x - 2)^2$ $\text{2) } y = x - 2$ Solution: Solve the system by substituting $y = (x - 2)^2$ into $y = x - 2$. $(x - 2)^2 = x - 2$

Let me know if you'd like detailed solutions for these systems!

Do you have any questions on the above? Here are five questions related to the topic:

1. How do you find the intersection points between a parabola and a line algebraically?
2. What methods can you use to solve a system of nonlinear equations?
3. How does the vertex form of a parabola help in determining its equation?
4. How do you interpret the slope of a line on a graph?
5. Why is it important to recognize the standard form of quadratic equations?

Tip: When solving a system of equations graphically, the points of intersection represent the solutions where the two equations are equal.