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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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