Equations in Two Variables
Definnition: An ordered pair of real numbers is a set of two elements in which one element is designated as the first element and the other the second. AX + BY = C where not both A and B are xero.By a solution to an equation in two variables we mean an ordered pair or real numbers such that when x is replaced by the first component of the ordered pair and y is replaced by the second component a true statement results. Example: (2, -5) is a solution of the equation 3x - 2y = 16 since we obtain the true statement 3(2) - 2(-5) = 16 or 6 + 10 = 16 or 16 = 16 when x is replaced by 2 and y is replaced by -5. Note (0,-8) is also a solution to the equation since 3(0) - 2(-8) = 16 is equaivalent to 0 + 16 = 16 which is equivalent to 16 = 16. In general an equation in two varibles may have an infinite number of solutions. Convention: In an equation in the two variables x and y, x is called the independent variable and y is called the dependent variable. In writing a solution to an equation in x and y as an ordered pair we always list the value of the indepent variable or value of x first, then the value of the dependent variable or value of y second. If confusion arises, remember to list the values of the variables in alphabetical order since x comes before y in the alphabet. To find solutions to an equation in two vaiables:
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