Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 4 - Sections 4.1-4.3 - Integrated Review - Systems of Linear Equations - Page 235: 21

Answer

Numbers are $19$ and $27$.

Work Step by Step

Let first number be $x$ and second number be $y$. First number is $8$ less than a second number. $x = y - 8$ $x - y = -8$ Equation $(1)$ Twice the first number is $11$ more than the second number. $2x = y + 11$ $2x - y = 11$ Equation $(2)$ Solving by elimination method, Multiply Equation (1) by $-1$ $-x +y = 8$ Equation $(3)$ Add Equation $(3)$ and Equation $(2)$ to eliminate $y$. $-x+2x+y-y=8+11$ $x = 19$ Substituting $x$ value in Equation $(1)$, to get $y$ $x - y = -8$ $x+8 = y$ $19 + 8 = y$ $y = 27$ First number is $19$ and Second number is $27$.
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