https://file.aiquickdraw.com/mathbot/file/1727363592712f2iwu5fr.jpg

The graph shows a system of two equations, one represented by a parabola and the other by a line. The solution to the system of equations is found at the points where the line intersects the parabola, as these are the points where both equations have the same \((x, y)\) values.

From the graph, we can observe that the line intersects the parabola at two points:
1. The first intersection appears to be at \( x = 0 \) and \( y = 4 \), giving the ordered pair \((0, 4)\).
2. The second intersection appears to be at \( x = 4 \) and \( y = 6 \), giving the ordered pair \((4, 6)\).

Thus, the solutions to the system are the ordered pairs:
\[
(0, 4) \quad \text{and} \quad (4, 6)
\]

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How can we algebraically find the solutions of a system involving a quadratic and a linear equation?
2. What methods can be used to solve systems of nonlinear equations graphically?
3. How does the shape of a parabola change based on its equation?
4. What is the general form of a quadratic equation, and how does it help in solving systems?
5. Can a system of a quadratic and linear equation have more than two solutions?

**Tip:** When solving systems graphically, make sure to check the coordinates carefully to avoid misinterpreting intersections.

What ordered pairs are the solutions of the system of equations shown in the graph?

Learn how to identify the solutions of a system of equations involving a quadratic and linear equation graphically. This problem covers key algebraic concepts, such as the intersection of a line and a parabola. Suitable for students in Grades 8-10.

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