This system has _____ solutions 1Infinitely 02 **Graph of a System of Linear Equations**This image shows a graph plotting two linear equations on a coordinate plane. The equations represented are:1. $ 6x - 4y = -12 $ (plotted as a blue line)2. $ 3x - 2y = -6 $ (plotted as a purple line)### Detailed Description of the Graph:- **Axes**: The graph uses a standard Cartesian coordinate system with the x-axis (horizontal) and y-axis (vertical). - **Scale**: The grid is marked in increments of 1 unit along both axes.- **Lines**: - The blue line representing the equation $ 6x - 4y = -12 $ is depicted moving diagonally from the bottom-left to the top-right of the graph. - The purple line representing the equation $ 3x - 2y = -6 $ also moves from the bottom-left to the top-right but is parallel and distinct from the blue line. The image also includes the following prompt for students to complete: **Q. This system has _________ solutions**### Interpretation:Since the two lines are parallel and do not intersect, this system of equations has no solutions. Parallel lines mean that the equations are dependent and inconsistent.### Key Points for students:- Understand how to plot linear equations on a graph.- Identify when lines are parallel by comparing slopes. Both lines here have the same slope.- Recognize that parallel lines indicate no solutions in a system of linear equations.

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This system has _____ solutions 1 Infinitely 0 2

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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Question

This system has _____ solutions 1 Infinitely 0 2

**Graph of a System of Linear Equations**

This image shows a graph plotting two linear equations on a coordinate plane. The equations represented are:

1. $ 6x - 4y = -12 $ (plotted as a blue line)
2. $ 3x - 2y = -6 $ (plotted as a purple line)

### Detailed Description of the Graph:
- **Axes**: The graph uses a standard Cartesian coordinate system with the x-axis (horizontal) and y-axis (vertical).
- **Scale**: The grid is marked in increments of 1 unit along both axes.
- **Lines**:
- The blue line representing the equation $ 6x - 4y = -12 $ is depicted moving diagonally from the bottom-left to the top-right of the graph.
- The purple line representing the equation $ 3x - 2y = -6 $ also moves from the bottom-left to the top-right but is parallel and distinct from the blue line.

The image also includes the following prompt for students to complete:

**Q. This system has _________ solutions**

### Interpretation:
Since the two lines are parallel and do not intersect, this system of equations has no solutions. Parallel lines mean that the equations are dependent and inconsistent.

### Key Points for students:
- Understand how to plot linear equations on a graph.
- Identify when lines are parallel by comparing slopes. Both lines here have the same slope.
- Recognize that parallel lines indicate no solutions in a system of linear equations.

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