Explanation Given Information: The system of equations y = − 2 and x − 2 y = 10 . Formula Used: Slope-intercept form: y = m x + b where m is the slope of the line and b is the y -intercept. The solution to a system of linear equations in two variables would correspond to the intersection point of the graphs of the two equations. A system of linear equations in two variables has a unique solution if the lines have different slopes. The system would have an infinitely many solutions if both the equations have the same slope and the same y -intercept. The system would have no solution if both the equations have the same slope but different y -intercepts. Calculation: Consider the provided equations y = − 2 and x − 2 y = 10 . Rewrite the provided equations in slope-intercept form y = m x + b where m is the slope of the line and b is the y -intercept. The equation y = − 2 is in the slope intercept form. The equation x − 2 y = 10 can be written as: x − 2 y = 10 − 2 y = − x + 10 y = 1 2 x − 5 The slope intercept form of the equation x − 2 y = 10 is y = 1 2 x − 5 . The line y = − 2 is parallel to the y -axis and has slope 0. The line y = 1 2 x − 5 has a slope 1 2 and y -intercept as − 5 . As the slopes are not the same, there exists a unique solution to the system of equations. Set up a table of coordinates for the equation y = − 2 : x y = − 2 0 − 2 4 − 2 Set up a table of coordinates for the equation y = 1 2 x − 5 : x y = 1 2 x − 5 3 − 3

Aleks 360 Access Card (18 Weeks) for Beginning & Intermediate Algebra

4th Edition

ISBN: 9780077564018

Author: ALEKS Corporation

Publisher: MCG

See similar textbooks

Videos

Question

Chapter 4.1, Problem 38PE

To determine

To calculate: The solution to the system y=−2 and x−2y=10 using the graphing method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.1, Problem 37PE

Chapter 4.1, Problem 39PE

Chapter 4 Solutions

Aleks 360 Access Card (18 Weeks) for Beginning & Intermediate Algebra

Ch. 4.1 - Determine whether the ordered paired is a solution...Ch. 4.1 - Determine whether the ordered paired is a solution...Ch. 4.1 - Solve the system by the graphing method. y = − 3 x...Ch. 4.1 - Solve the system by the graphing method. y = 2 x −...Ch. 4.1 - Solve the system by the graphing. 5. Ch. 4.1 - Solve the system by the graphing. 6. Ch. 4.1 - a. A______ of linear equations consists of two or...Ch. 4.1 - For Exercises 2-10, determine if the given point...Ch. 4.1 - Prob. 3PE Ch. 4.1 - Prob. 4PE

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The solution to the system y = − 2 and x − 2 y = 10 using the graphing method.

Solution Summary: The author calculates the solution to a system of linear equations in two variables using the graphing method.

Videos

To calculate: The solution to the system y=−2 and x−2y=10 using the graphing method.

Want to see the full answer?

Chapter 4 Solutions