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Expert-verified Found in: Page 612 ### Elementary Algebra

Book edition 2nd
Author(s) Lynn Marecek, MaryAnne Anthony-Smith
Pages 1240 pages
ISBN 9780998625713 # In the following exercises, translate to a system of equations and solve.The sum of two numbers is 15. One number is 3 less than the other. Find the numbers.

The numbers are 6 and 9

See the step by step solution

## Step 1. Given Information

The given data is that the sum of two numbers is 15. One number is 3 less than the other.

## Step 2. Calculation

Let us assume that x be the first number and y be the second number.

The sum of two number is 15 implies that $x+y=15--\left(1\right)$

One number is 3 less than the other implies that $x=y-3--\left(2\right)$

Substitute the value of variable x from equation (2) in equation (1).

localid="1647449889617" $x+y=15\phantom{\rule{0ex}{0ex}}y-3+y=15\phantom{\rule{0ex}{0ex}}2y=18\phantom{\rule{0ex}{0ex}}y=9\phantom{\rule{0ex}{0ex}}$

Find the value of variable x by using the obtained value of y.

localid="1647449918198" $x=y-3\phantom{\rule{0ex}{0ex}}x=9-3\phantom{\rule{0ex}{0ex}}x=6$

Thus, the required ordered pair is $\left(9,6\right)$ ### Want to see more solutions like these? 