Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - Guided Practice for Examples 3 and 4 - Page 207: 5

Answer

$x=-1,y=3$

Work Step by Step

We know that for a matrix \[ \left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right] \] the determinant is $D=ad-bc.$ Thus the determinant of the coefficient matrix is: $D=3\cdot5-(-4)\cdot2=15+8=23.$ Then applying Cramer's Rule: $x=\frac{\begin{vmatrix} -15 & -4 \\ 13 & 5 \\ \end{vmatrix}}{23}=\frac{-15\cdot5-(-4)\cdot13}{23}=\frac{-23}{23}=-1$ $y=\frac{\begin{vmatrix} 3 & -15 \\ 2 & 13 \\ \end{vmatrix}}{23}=\frac{3\cdot13-(-15)\cdot2}{23}=\frac{69}{23}=3$ Thus $x=-1,y=3$
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