Algebra: A Combined Approach (4th Edition)

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

Chapter 4 - Test - Page 331: 17

Answer

$$x=-5$$ $$y=3$$

Work Step by Step

Equation 1: $0.01x - 0.06y = -0.23$ Equation 2: $0.2x + 0.4y = 0.2$ Using equation 2, subtract $0.2x$ from both sides: $$0.2x + 0.4y = 0.2$$ $$0.2x -0.2x+ 0.4y = 0.2-0.2x$$ $$0.4y = 0.2-0.2x$$ Divide both sides by $0.4$: $$\frac{0.4y}{0.4} = \frac{0.2-0.2x}{0.4}$$ $$y = 0.5-0.5x$$ Substitute this equation to equation 1: $$0.01x - 0.06(0.5-0.5x) = -0.23$$ $$0.01x - 0.03+0.03x= -0.23$$ $$0.04x-0.03=-0.23$$ Add $0.03$ to both sides: $$0.04x-0.03+0.03=-0.23+0.03$$ $$0.04x=-0.20$$ Divide both sides by $0.04$: $$\frac{0.04x}{0.04}=\frac{-0.20}{0.04}$$ $$x=-5$$ Substitute this value of $x$ to equation 2: $$0.2x + 0.4y = 0.2$$ $$0.2(-5) + 0.4y = 0.2$$ $$-1 + 0.4y = 0.2$$ Add $1$ to both sides: $$-1+1 + 0.4y = 0.2+1$$ $$0.4y = 1.2$$ Divide both sides $0.4$: $$\frac{0.4y}{0.4} =\frac{1.2}{0.4}$$ $$y=3$$ Check using equation 1: $$0.01x - 0.06y = -0.23$$ $$0.01(-5) - 0.06(3) = -0.23$$ $$-0.05 - 0.18 = -0.23$$ $$-0.23=-0.23$$
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