Algebra: A Combined Approach (4th Edition)

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

Chapter 4 - Review - Page 328: 17

Answer

True for all values of $x$ and $y$.

Work Step by Step

equation 1 $$4y = 2x + 6$$ equation 2 $$x - 2y = -3$$ Using equation 2, add $2y$ to both sides: $$x - 2y = -3$$ $$x - 2y +2y= -3+2y$$ $$x = -3+2y$$ We will refer to $x = -3+2y$ as equation $2'$. Substitute equation 2' to equation 1: $$4y = 2x + 6$$ $$4y = 2(-3+2y) + 6$$ $$4y = -6+4y + 6$$ $$4y = 4y$$ Since the equation is true, then the equation is true for all values of $y$. Now, let's solve for $x$. Using equation 2, subtract $x$ from both sides: $$x - 2y = -3$$ $$x -x- 2y = -3-x$$ $$- 2y = -3-x$$ Divide both sides by $-2$. $$\frac{-2y}{-2} = \frac{-3-x}{-2}$$ $$y=\frac{-3-x}{-2}$$ $$y=\frac{3+x}{2}$$ Substitute this to equation 1: $$4y = 2x + 6$$ $$4(\frac{3+x}{2}) = 2x + 6$$ $$2(3+x)= 2x + 6$$ $$6+2x= 2x + 6$$ Hence, the equation is also true for all values of $x$.
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