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

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Author: Miller

Publisher: MCG

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Chapter 4.1, Problem 38PE

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

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Chapter 4.1, Problem 37PE

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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.

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