Stitz-Zeager_College_Algebra_e-book

We rst encode the system into a matrix pay attention

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Unformatted text preview: 1, the graphs of linear equations are lines. If we couple two or more linear equations together, in effect to find the points of intersection of two or more lines, we obtain a system of linear equations in two variables. Our first example reviews some of the basic techniques first learned in Intermediate Algebra. Example 8.1.1. Solve the following systems of equations. Check your answer algebraically and graphically. 1. 2. 2x − y = 1 y=3 3x + 4y = −2 −3x − y = 5 3. 4. 4y x 3− 5 y 2x 9 +3 = = 7 5 1 2 2x − 4y = 6 3x − 6y = 9 6x + 3y = 9 4x + 2y = 12 5. 6. x−y = 0 x+y = 2 −2x + y = −2 Solution. 1. Our first system is nearly solved for us. The second equation tells us that y = 3. To find the corresponding value of x, we substitute this value for y into the the first equation to obtain 2x − 3 = 1, so that x = 2. Our solution to the system is (2, 3). To check this algebraically, we substitute x = 2 and y = 3 into each equation and see that they are satisfied. We see 2(2) − 3 = 1, and 3 = 3, as required. To...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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