Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 6 - Systems of Equations and Inequalities - Chapter Test - Page 411: 16


y=3x+82 y=3x-10

Work Step by Step

Lets solve this system so we can understand why there are no solutions that satisfy both the equations. We will use substitution as our method of solving this problem First lets substitute the value of y, (3x-10), in the second equation to the y term in the first equation. 3x-8=3x-10 (add 8 to both sides of the equation) 3x=3x-2 (Subtract 3x from both sides of the equation) 0=-2 The statement above, 0=-2, is never true so therefore there are not any solutions/points that satisfy both the equations above. Here is another way to figure out that there are no solutions to the system: We can graph the two equations above and see that their graphs are parallel and never intersect each other. When graphs of equation do not intersect each other, we can assert that there are no solutions to the system.
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