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What ordered pairs are the solutions of the system of equations shown in the graph below? 10 8 -8 6 F4 6 8 -10 -2 4 10 -2 -4 -6 -8 -10 and (

What ordered pairs are the solutions of the system of equations shown in the graph below? 10 8 -8 6 F4 6 8 -10 -2 4 10 -2 -4 -6 -8 -10 and (

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Graphing Systems of Equations: Identifying Solutions #### Problem Statement **What ordered pairs are the solutions of the system of equations shown in the graph below?** #### Graph Description The graph provided shows the Cartesian coordinate plane with a system of two equations plotted on it. The graph is divided by a horizontal x-axis and a vertical y-axis, each labeled accordingly with values ranging from -10 to 10. 1. **Line Graph**: The first equation is represented by a straight line that crosses the y-axis at y = 10 and intersects the x-axis at approximately x = -2. This line extends diagonally from the upper left to the lower right side of the graph. 2. **Parabola**: The second equation is represented by a parabola that opens downwards. The vertex (highest point) of the parabola appears to be located to the left of the y-axis, approximately at the point (-4, 2). The arms of the parabola curve downwards, crossing the x-axis at approximately x = -2 and x = -6, and pass through the y-axis between y = 0 and y = -10. #### Intersections The solutions to the system of equations are the points where the two graphs intersect. According to the graph: - The first point of intersection appears to be around (-6, -8). - The second point of intersection appears to be around (-2, 4). #### Answer Submission Below the graph, two boxes are provided to input the ordered pairs (x, y) that represent the solutions to the system of equations. ```plaintext ( [ ] , [ ] ) and ( [ ] , [ ] ) Submit Answer [Button] ``` Verify the points by analyzing where the line intersects the parabola. This graph visually aids in understanding how different types of equations can intersect in the coordinate plane, providing a graphical solution to a system of equations.
Transcribed Image Text:### Graphing Systems of Equations: Identifying Solutions #### Problem Statement **What ordered pairs are the solutions of the system of equations shown in the graph below?** #### Graph Description The graph provided shows the Cartesian coordinate plane with a system of two equations plotted on it. The graph is divided by a horizontal x-axis and a vertical y-axis, each labeled accordingly with values ranging from -10 to 10. 1. **Line Graph**: The first equation is represented by a straight line that crosses the y-axis at y = 10 and intersects the x-axis at approximately x = -2. This line extends diagonally from the upper left to the lower right side of the graph. 2. **Parabola**: The second equation is represented by a parabola that opens downwards. The vertex (highest point) of the parabola appears to be located to the left of the y-axis, approximately at the point (-4, 2). The arms of the parabola curve downwards, crossing the x-axis at approximately x = -2 and x = -6, and pass through the y-axis between y = 0 and y = -10. #### Intersections The solutions to the system of equations are the points where the two graphs intersect. According to the graph: - The first point of intersection appears to be around (-6, -8). - The second point of intersection appears to be around (-2, 4). #### Answer Submission Below the graph, two boxes are provided to input the ordered pairs (x, y) that represent the solutions to the system of equations. ```plaintext ( [ ] , [ ] ) and ( [ ] , [ ] ) Submit Answer [Button] ``` Verify the points by analyzing where the line intersects the parabola. This graph visually aids in understanding how different types of equations can intersect in the coordinate plane, providing a graphical solution to a system of equations.
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