Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 3 - Mid-Chapter Check Point - Page 220: 5


$\{\left (\frac{11}{19},\frac{7}{19} \right )\}$.

Work Step by Step

The given system of equations are $\Rightarrow 2x+5y=3$......(1) $\Rightarrow 3x-2y=1$......(2) Multiply equation (1) by 2 and equation (2) by 5 and then add. $\Rightarrow 2(2x+5y)+5(3x-2y)=2(3)+5(1)$ Simplify. $\Rightarrow 4x+10y+15x-10y=6+5$ Add like terms. $\Rightarrow 19x=11$ Divide both sides by $19$. $\Rightarrow \frac{19x}{19}=\frac{11}{19}$ Simplify. $\Rightarrow x=\frac{11}{19}$ Substitute the value of $x$ into equation (1). $\Rightarrow 2(\frac{11}{19})+5y=3$ Simplify. $\Rightarrow \frac{22}{19}+5y=3$ Multiply the equation by $19$ $\Rightarrow 19\cdot \left ( \frac{22}{19}+5y \right )=19\cdot (3)$ Apply distributive property. $\Rightarrow 22+95y=57$ Subtract $22$ from both sides. $\Rightarrow 22+95y-22=57-22$ Add like terms. $\Rightarrow 95y=35$ Divide both sides by $95$ $\Rightarrow \frac{95y}{95}=\frac{35}{95}$ Simplify. $\Rightarrow y=\frac{7}{19}$ The solution set is $\{\left (x,y \right )\}=\{\left (\frac{11}{19},\frac{7}{19} \right )\}$.
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