OBJECTIVE: To obtain the conditions for consistency or inconsistency of a system of linear equations in two variables by graphical method.
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To verify the conditions for consistency of a system of linear equations in two variables by graphical representation. An equation of the form ax+by+c = 0, where a, b, c are real numbers, a≠0, b≠0 and x, y are variables; is called a linear equation in two variables.
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if the two lines intersect at a point then the system is consistent and has a unique solution. if the two lines are coincident then the system is consistent and has infinitely many solutions. if the two lines are parallel to each other then the system is inconsistent and has no solution.
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