Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 4 - Review - Page 329: 43

Answer

$$x = -5$$ $$y=2$$

Work Step by Step

Equation 1: $x - 3y = -11$ Equation 2: $4x + 5y = -10$ Using equation 1, add $3y$ to both sides: $$x - 3y +3y= -11+3y$$ $$x = -11+3y$$ Substitute this equation to equation 2: $$4x + 5y = -10$$ $$4(-11+3y) + 5y = -10$$ $$-44+12y + 5y = -10$$ $$-44+17y= -10$$ Add $44$ to both sides: $$-44+44+17y= -10+44$$ $$17y=34$$ $$y=2$$ Substitute this value of $y$ to equation 1: $$x - 3y = -11$$ $$x - 3(2) = -11$$ $$x - 6 = -11$$ Add $6$ to both sides: $$x - 6+6 = -11+6$$ $$x = -5$$ Use equation 2 to check: $$4x + 5y = -10$$ $$4(-5) + 5(2) = -10$$ $$-20 + 10 = -10$$ $$-10=-10$$
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