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Linear Equations in Two Variables

Linear Equations in Two VariablesIn this chapter, we ll use the geometry of lines to help us solve Equations in two variablesIfa,b,andrare real numbers (and ifaandbare not both equal to 0) thenax+by=ris called alinear equation in two Variables . (The two Variables are thexand they.)The numbersaandbare called thecoe cientsof the equationax+by= numberris called theconstantof the equationax+by= 3y=5and 2x 4y= 7 are Linear Equations in of equationsAsolutionof a Linear equation in two variablesax+by=ris a specific pointinR2such that when when thex-coordinate of the point is multiplied bya,and they-coordinate of the point is multiplied byb, and those two numbersare added together, the answer equalsr. (There are always infinitely manysolutions to a Linear equation in two Variables .)

A solution of a system of equations is a point that is a solution of each of the equations in the system. Example. The point x =3andy =2isasolutionofthesystemoftwo linear equations in two variables 8x +7y =38 3x 5y = 1 because x =3andy =2isasolutionof3x5y = 1 and it is a solution of

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