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# Lesson32 - MA 15200 Lesson 32 Section 5.1 A linear equation...

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1 MA 15200 Lesson 32, Section 5.1 A linear equation with two variables has infinite solutions (many ordered pairs, example 6 3 2 = - y x ) However, if a second equation is also considered, and we want to know what ordered pairs they may have in common, how many solutions may there be? When two linear equations are considered together, it is known as a system of linear equations or a linear system. The solution(s) of the system is/are any ordered pair(s) they have in common. Consider graphing two lines. How many points may they have in common? As demonstrated in the graphs above, there are 3 situations. 1. The graphs may intersect at one point. If the lines of the equations intersect, the solution is one ordered pair. 2. The graphs may intersect at an infinite number of points. If the lines of the equations form the same line, the solution is an infinite number of ordered pairs. 3. The graphs may not intersect. If the lines of the equations do not intersect, there is no solution. Ex 1: Given the ordered pair, determine if it is a solution of the shown system. 2 5 16 ) ( 2,4) 3 2 5 2 1 3 ) ,1 10 5 1 5 x y a x y x y b x y + = - + = - + = + = If an ordered pair is a solution of the system of equations, it is a solution of both equations. In other words, substituted in both equations yields a true statement.

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Lesson32 - MA 15200 Lesson 32 Section 5.1 A linear equation...

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