Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 742: 22

Answer

$(x,y) =(2,3)$

Work Step by Step

The given system of equations is $\left\{\begin{matrix} 2x& +&4y&=&16\\ 3x& -&5y & =&-9 \end{matrix}\right.$ Determinant $D$ consists of the $x$ and $y$ coefficients. $D=\begin{vmatrix} 2&4 \\ 3& -5 \end{vmatrix}=(2)(-5)-(3)(4)=-10-12=-22$ For determinant $D_x$ replace the $x−$ coefficients with the constants. $D_x=\begin{vmatrix} 16&4 \\ -9& -5 \end{vmatrix}=(16)(-5)-(-9)(4)=-80+36=-44$ For determinant $D_y$ replace the $y−$ coefficients with the constants. $D_y=\begin{vmatrix} 2&16 \\ 3& -9 \end{vmatrix}=(2)(-9)-(3)(16)=-18-48=-66$ By using Cramer's rule we have. $x=\dfrac{D_x}{D}=\dfrac{-44}{-22}=2$ and $y=\dfrac{D_y}{D}=\dfrac{-66}{-22}=3$ Hence, the solution is $(x,y) =(2,3)$.
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