Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 10 - Section 10.1 - Systems of Linear Equations in Two Variables - 10.1 Exercises - Page 688: 6

Answer

$x=1$ $y=-2$

Work Step by Step

$\begin{cases} 3x+y=1\\5x+2y=1\end{cases}$ Let $3x+y=1$ be equation 1 and $5x+2y=1$ be equation 2 Solve for $y$ in equation 1: $3x+y=1$ $y=1-3x$ Let this equation be equation 3 Substitute equation 3 in equation 2: $5x+2y=1$ $5x+2(1-3x)=1$ Simplify and solve for $x$: $5x+2-6x=1$ $-x=-1$ $x=1$ Finally, substitute $x=1$ in equation 3: $y=1-3x$ $y=1-3(1)=-2$
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