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 a System of Linear Equations**
To graph the system of linear equations, follow the steps below:
**System of Equations:**
1. \(4x + 2y = -12\)
2. \(3x + y = -10\)
**Instructions:**
1. **Solve for \(y\) in each equation to find the slope-intercept form (\(y = mx + b\))**:
- For \(4x + 2y = -12\):
\[
2y = -4x - 12
\]
\[
y = -2x - 6
\]
- For \(3x + y = -10\):
\[
y = -3x - 10
\]
2. **Plot each line on the graph**:
- The graph is a coordinate plane with labeled axes ranging from -6 to 6 on both the x and y axes.
- **Line \(y = -2x - 6\)**:
- The y-intercept is \(-6\) (plot point at (0, -6)).
- The slope is \(-2\) (from the intercept, go down 2 units and right 1 unit for additional points).
- **Line \(y = -3x - 10\)**:
- The y-intercept is \(-10\) (plot point at (0, -10)).
- The slope is \(-3\) (from the intercept, go down 3 units and right 1 unit for additional points).
3. **Find the point of intersection**:
- Graphically, identify where the two lines intersect, solving the system. This represents the solution to the system.
By following these steps, you can create an accurate graph of the system of equations and determine the intersection point visually.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47233639-9d53-42f0-bc37-bcddb016235d%2F1e77d480-aebe-49ef-aeb7-06ad21da30e2%2F0yrx5b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphing a System of Linear Equations**
To graph the system of linear equations, follow the steps below:
**System of Equations:**
1. \(4x + 2y = -12\)
2. \(3x + y = -10\)
**Instructions:**
1. **Solve for \(y\) in each equation to find the slope-intercept form (\(y = mx + b\))**:
- For \(4x + 2y = -12\):
\[
2y = -4x - 12
\]
\[
y = -2x - 6
\]
- For \(3x + y = -10\):
\[
y = -3x - 10
\]
2. **Plot each line on the graph**:
- The graph is a coordinate plane with labeled axes ranging from -6 to 6 on both the x and y axes.
- **Line \(y = -2x - 6\)**:
- The y-intercept is \(-6\) (plot point at (0, -6)).
- The slope is \(-2\) (from the intercept, go down 2 units and right 1 unit for additional points).
- **Line \(y = -3x - 10\)**:
- The y-intercept is \(-10\) (plot point at (0, -10)).
- The slope is \(-3\) (from the intercept, go down 3 units and right 1 unit for additional points).
3. **Find the point of intersection**:
- Graphically, identify where the two lines intersect, solving the system. This represents the solution to the system.
By following these steps, you can create an accurate graph of the system of equations and determine the intersection point visually.
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