Consider the straight line x + y = 1 and the family of straight lines that pass through the origin given by y = mx. As m changes the line rotates about the origin. a) Solve the system of equations for m = 1, which makes it x+y = 1 and y = x b) Solve the system of equations for m = 2, which makes it x+y=1 and y = 2x c) Solve these two systems of linear equation in general which is using m as a constant and find their points of intersection. Is there always a solution - If yes, briefly explain why. If not - for what values of m is there no solution.
Consider the straight line x + y = 1 and the family of straight lines that pass through the origin given by y = mx. As m changes the line rotates about the origin. a) Solve the system of equations for m = 1, which makes it x+y = 1 and y = x b) Solve the system of equations for m = 2, which makes it x+y=1 and y = 2x c) Solve these two systems of linear equation in general which is using m as a constant and find their points of intersection. Is there always a solution - If yes, briefly explain why. If not - for what values of m is there no solution.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter7: Conic Sections And Quadratic Systems
Section7.4: Solving Nonlinear Systems Of Equations
Problem 63E
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Question
Consider the straight line x + y = 1 and the family of straight lines that pass
through the origin given by y = mx. As m changes the line rotates about the
origin.
a) Solve the system of equations for m = 1, which makes it x+y = 1 and y =
x
b) Solve the system of equations for m = 2, which makes it x+y=1 and y = 2x
c) Solve these two systems of linear equation in general which is using m as a
constant and find their points of intersection. Is there always a solution - If
yes, briefly explain why. If not - for what values of m is there no solution.
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