Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 10 - Systems of Equations and Inequalities - Section 10.1 Systems of Linear Equations: Substitution and Elimination - 10.1 Assess Your Understanding - Page 734: 31

Answer

$x= 1, y= 1 \text{ or } (1, 1)$

Work Step by Step

The system of equations is given by the following two equations: $$\begin{cases} 2x-3y=-1\hspace{20pt} (1)\\[3mm] 10x+y=11 \hspace{20pt} (2) \end{cases}$$ Multiplying equation $(2)$ by $3$ so that the coefficients of y in the two equations are additive inverses gives: $30x+3y=33\hspace{20pt} (1)$ $\text{Add the two equations to eliminate y}$ \[ \begin{aligned} 2x-3y&=-1 \\[2mm] 30x+3y&=33 \ \\[3mm] \hline 32x&=32\\[2mm] \end{aligned} \] Divide $32$ to both sides to obtain: $x=1$ $\text{Substituting in equation (2) for }x=1$ gives: $10(1)+y=11$ $10+y=11$ $y=1$ Therefore, the solution is: $\boxed{x= 1 \hspace{20pt} y= 1}$
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