Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises - Page 10: 33

Answer

b.) The system is consistent according to the graph. c.) The solution is approximately $x = \frac{1}{2}, y = -\frac{1}{4}$. d.) By adding -1/4 times Equation 1 to Equation 2, we can then solve that $y = -\frac{1}{4}$. Through back substitution, we can solve that $x = \frac{1}{2}$. e.) Both solutions are identical, we can conclude that the system is consistent and the solution is $x = \frac{1}{2}, y = -\frac{1}{4}$.
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Work Step by Step

b.) By graphing the equations, we can see that they intersect and are therefore consistent. d.) By adding $-\frac{1}{4}$ times Equation 1 to Equation 2, we can then eliminate the $x$ variable in Equation 2. $2x -8y = 3$ $0x + 3y = -\frac{3}{4}$ We can then conclude from the modified Equation 2, that $y = -\frac{1}{4}$. This value can then be substituted into Equation 1 to then solve for $x$. $2x-8*(-\frac{1}{4}) = 3$ $2x = 1$ $x = \frac{1}{2}$
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