Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 8 - Coordinate Geometry and Linear Systems - 8.6 - Elimination-by-Addition Method - Problem Set 8.6: 59

Answer

The answer is below.

Work Step by Step

We first isolate x in both equations: For equation one: $ a_1 x = c_1 - b_1y \\ x = \frac{c_1 - b_1y}{a_1}$ Doing the same thing for equation two yields: $ x = \frac{c_2 - b_2y}{a_2}$ Combining these and cross multiplying gives: $a_2c_1 - a_2b_1y =a_1c_2 - a_1b_2y \\ $ Solving for y gives: $ y = \frac{a_2c_1 - a_1c_2}{a_2b_1 - a_1b_2}$ Plugging this in for y and simplifying gives an x value of: $x = \frac{ b_1c_2 - b_2c_1}{a_2b_1 - a_1b_2}$
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