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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Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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![**Solving a System of Equations Graphically**
In this exercise, you'll learn how to solve a system of equations by graphically representing them and determining the points of intersection.
**Problem Statement**
Solve the following system of equations graphically and state the coordinates of all points in the solution set:
1. \( y = x^2 + 4x - 5 \)
2. \( y = x - 1 \)
**Solution Steps**
To solve this system of equations graphically, follow these steps:
1. **Graph the equations**:
- Plot the first equation \( y = x^2 + 4x - 5 \), which represents a parabola.
- Plot the second equation \( y = x - 1 \), which represents a straight line.
2. **Identify the points of intersection**:
- The solution to the system of equations is the coordinates where the graphs intersect.
**Answer:**
The coordinates of the points in the solution set are:
\[ (\_\_\_\_, 0) \]
and
\[ (\_\_\_\_, \_\_\_\_) \]
**Graph Explanation**
- The first equation, \( y = x^2 + 4x - 5 \), is a parabola that opens upwards.
- The second equation, \( y = x - 1 \), is a linear function with a slope of 1 and y-intercept at -1.
By plotting these graphs, we find the points where they intersect, which gives us the solution to the system of equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa9e202f-d9ce-40dc-9837-4f4bc2a0b860%2F16f30b18-61db-47e0-94db-9e7aa586139b%2F2486uza_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving a System of Equations Graphically**
In this exercise, you'll learn how to solve a system of equations by graphically representing them and determining the points of intersection.
**Problem Statement**
Solve the following system of equations graphically and state the coordinates of all points in the solution set:
1. \( y = x^2 + 4x - 5 \)
2. \( y = x - 1 \)
**Solution Steps**
To solve this system of equations graphically, follow these steps:
1. **Graph the equations**:
- Plot the first equation \( y = x^2 + 4x - 5 \), which represents a parabola.
- Plot the second equation \( y = x - 1 \), which represents a straight line.
2. **Identify the points of intersection**:
- The solution to the system of equations is the coordinates where the graphs intersect.
**Answer:**
The coordinates of the points in the solution set are:
\[ (\_\_\_\_, 0) \]
and
\[ (\_\_\_\_, \_\_\_\_) \]
**Graph Explanation**
- The first equation, \( y = x^2 + 4x - 5 \), is a parabola that opens upwards.
- The second equation, \( y = x - 1 \), is a linear function with a slope of 1 and y-intercept at -1.
By plotting these graphs, we find the points where they intersect, which gives us the solution to the system of equations.
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