If the graphs of the two linear equations have different slopes, how many solutions does the related system have? Give a verbal and a graphical justification for your answer.
Answer to Problem 4C
There will be onesolution, if the graphs of the two linear equations have different slopes.
Explanation of Solution
We know that if the graphs of two linear equations have different slopes, then they will intersect exactly in one place.
We also know that the solution of a system of equation is the point, where the graphs of both equations intersect.
Let us assume that our system of equations is
Let us graph our given system of equations. We can see that both equations are in slope-intercept form.
Upon graphing both equations, we will get our required graph as shown below:
Upon looking at our graph, we can see that both lines intersect at point
Chapter 8 Solutions
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Additional Math Textbook Solutions
Algebra and Trigonometry
College Algebra
Intermediate Algebra (7th Edition)
College Algebra with Modeling & Visualization (5th Edition)
A Graphical Approach to College Algebra (6th Edition)
College Algebra with Modeling & Visualization (6th Edition)
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education