Chapter 11: Q. 30 (page 794)

Use Cramer’s 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

Step 1. The given information is

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

Step 2. Finding the determinant

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

hence using crammer's rule

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

Step 3. Finding Dx and Dy we get

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

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

Short Answer

Step by step solution

Step 1. The given information is

Step 2. Finding the determinant

Step 3. Finding Dx and Dy we get

Step 4. Solving for x and y we get

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Use Cramer’s Rule, if applicable, to solve each system.2x+3y-13=03x-2y=0

Short Answer

Step by step solution

Step 1. The given information is

Step 2. Finding the determinant

Step 3. Finding Dx and Dy we get

Step 4. Solving for x and y we get

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

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