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ss_10_1 - Section 10.1 Systems of Linear Equations in Two...

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Section 10.1 Systems of Linear Equations in Two Variables This section contains material on solving systems of linear equations in two variables. Recall that a linear equation in two variables is an equation of the form Ax + By = C ,where A , B ,and C are constants. Linear equations in the variables x and y have graphs that are lines in xy - space. We begin with an example that uses the process of elimination for simplifying and solving a system of two equations in two unknowns. In the example, the notation ( R 1+ R 2) indicates that Row 1 was added to Row 2 to obtain the current row. Example. Solve the following system 2 x + y =1 x +2 y =2 Solution. 2 x + y x y 2 x + y - 2 x - 4 y = - 4( - 2 R 2) 2 x + y 0 - 3 y = - 3( R R 2) 2 x + y y ( - 1 3 R 2) Hence y = 1. Since 2 x + y =1and y =1,2 x =0and x =0. The following figure gives a graphical solution of the above system. The plot of each of the two linear equations is a straight line. The solution of the system must satisfy both equations and hence must lie on both the lines. –2 2 4 –2 –1 1 2 x General system of m equations in two variables a 11 x + a 12 y = b 1 a 21 x + a 22 y = b 2 ··· a m 1 x + a m 2 y = b m
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ss_10_1 - Section 10.1 Systems of Linear Equations in Two...

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