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Which of the following shows the solution(s) for this system of equations?  A. (-3, 0) and (3, 0)  B. (-2, 4) and (2, 4)   C. There are no solutions   D. (0, 8) 

To solve this system of equations, we need to identify where the two curves intersect.

The two equations are:
1. \( y = x^2 \) (a parabola)
2. \( y = 4 \) (a horizontal line)

The solution(s) will be the points where the graphs of these two equations intersect. From the graph:

- The parabola \( y = x^2 \) opens upwards and passes through the origin.
- The line \( y = 4 \) is a horizontal line.

To find the intersections, we set the two equations equal to each other:

\[
x^2 = 4
\]

Solving for \( x \):

\[
x = \pm 2
\]

Thus, the points of intersection are \( (-2, 4) \) and \( (2, 4) \).

Therefore, the correct answer is **B. (-2, 4) and (2, 4)**.

Would you like any more details or have questions?

Here are five related questions you might find useful:
1. What are the steps to solve a system of non-linear equations algebraically?
2. How do you determine the number of solutions for a quadratic and linear system?
3. What other methods can be used to solve a system of equations graphically?
4. Can the quadratic equation have fewer or more than two solutions when intersecting a line?
5. How does the vertex of a parabola help in identifying possible solutions?

**Tip:** Always check both algebraic and graphical solutions to confirm the accuracy of intersections.

Which of the following shows the solution(s) for this system of equations? A. (-3, 0) and (3, 0) B. (-2, 4) and (2, 4) C. There are no solutions D. (0, 8)

Learn how to solve a system of equations by finding the intersection points of y = x^2 and y = 4. This problem covers the core concepts of graphing quadratic functions and solving equations algebraically, suitable for Grades 8-10.

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