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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 30 (page 794)

Use Cramer鈥檚 Rule, if applicable, to solve each system.
$\{\begin{cases} 2 x + 3 y - 13 = 0 \\ 3 x - 2 y = 0 \end{cases}$

Short Answer

Expert verified

Ordered pair is $(2, 3)$

Step by step solution

01

Step 1. The given information is

$\{\begin{cases} 2 x + 3 y - 13 = 0 \\ 3 x - 2 y = 0 \end{cases}$

02

Step 2. Finding the determinant

$D = |\begin{matrix} 2 & 3 \\ 3 & - 2 \end{matrix}| D = 2 (- 2) - (3) (3) D = - 4 - 9 D = - 13 D 鈮� 0$

hence using crammer's rule

$x = \frac{D_{x}}{D}, y = \frac{D_{y}}{D}$

03

Step 3. Finding Dx and Dy we get

$D_{x} = |\begin{matrix} 13 & 3 \\ 0 & - 2 \end{matrix}| D_{x} = 13 (- 2) - 0 (3) D_{x} = - 26 D_{y} = |\begin{matrix} 2 & 13 \\ 3 & 0 \end{matrix}| D_{y} = 2 (0) - 13 (3) D_{y} = - 39$

04

Step 4. Solving for x and y we get

$x = \frac{D_{x}}{D} x = \frac{- 26}{- 13} x = 2 y = \frac{D_{y}}{D} y = \frac{- 39}{- 13} y = 3$

Ordered pair is $(2, 3)$

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