Explanation Given Information: The system of equations 3 x + 3 y = 3 and 2 x − y = 5 . 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 3 x + 3 y = 3 and 2 x − y = 5 . 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 3 x + 3 y = 3 can be written as: 3 x + 3 y = 3 x + y = 1 y = − x + 1 The slope intercept form of the equation 3 x + 3 y = 3 is y = − x + 1 . The equation 2 x − y = 5 can be written as: 2 x − y = 5 − y = − 2 x + 5 y = 2 x − 5 The slope intercept form of the equation 2 x − y = 5 is y = 2 x − 5 . The line y = − x + 1 has slope as − 1 and y- intercept as 1. The line y = 2 x − 5 has slope 2 and y -intercept as − 5 . As the lines have different slopes, the system would have a unique solution. Set up a table of coordinates for the equation y = − x + 1 : x y = − x + 1 − 1 2 3 − 2 Set up a table of coordinates for the equation y = 2 x − 5 : x y = 2 x − 5 3 1 0 − 5 Graph: The graph of the lines is shown below:

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ISBN: 9781259616754

Author: Julie Miller, Molly O'Neill, Nancy Hyde

Publisher: McGraw-Hill Education

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Chapter 4.1, Problem 46PE

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To calculate: The solution to the system 3x+3y=3 and 2x−y=5 using the graphing method.

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Chapter 4.1, Problem 45PE

Chapter 4.1, Problem 47PE

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Chapter 4 Solutions

Beginning and 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

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

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To calculate: The solution to the system 3x+3y=3 and 2x−y=5 using the graphing method.

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Chapter 4 Solutions