Chapter 11: Q. 29 (page 794)

Use Cramer’s Rule, if applicable, to solve each system.
$\{\begin{cases} x - 2 y = 4 \\ 3 x + 2 y = 4 \end{cases}$

Short Answer

Expert verified

Ordered pair is $(2, - 1)$

Step by step solution

Step 1. Given information is

$\{\begin{cases} x - 2 y = 4 \\ 3 x + 2 y = 4 \end{cases}$

Step 2. Finding determinants we get,

$D = |\begin{matrix} 1 & - 2 \\ 3 & 2 \end{matrix}| D = (1) (2) - (- 2) (3) D = 2 + 6 D = 8 D \neq 0$

Using crammer's rule we get $x = \frac{D_{x}}{D}, y = \frac{D_{y}}{D}$

Step 3. Solving for Dx, Dy we get

$D_{x} = |\begin{matrix} 4 & - 2 \\ 4 & 2 \end{matrix}| D_{x} = 4 (2) - (- 2) (4) D_{x} = 8 + 8 D_{x} = 16$

$D_{y} = |\begin{matrix} 1 & 4 \\ 3 & 4 \end{matrix}| D_{y} = (1) (4) - (4) (3) D_{y} = 4 - 12 D_{y} = - 8$

Step 4. Now value of x and y

$x = \frac{D_{x}}{D} x = \frac{16}{8} x = 2 y = \frac{D_{y}}{D} y = \frac{- 8}{8} y = - 1$

The ordered pair we have is $(2, - 1)$

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Use Cramer’s Rule, if applicable, to solve each system.
$\{\begin{cases} x - 2 y = 4 \\ 3 x + 2 y = 4 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information is

Step 2. Finding determinants we get,

Step 3. Solving for Dx, Dy we get

Step 4. Now value of x and y

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Use Cramer’s Rule, if applicable, to solve each system.x-2y=43x+2y=4

Short Answer

Step by step solution

Step 1. Given information is

Step 2. Finding determinants we get,

Step 3. Solving for Dx, Dy we get

Step 4. Now value of x and y

One App. One Place for Learning.

Most popular questions from this chapter

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Use Cramer’s Rule, if applicable, to solve each system.
$\{\begin{cases} x - 2 y = 4 \\ 3 x + 2 y = 4 \end{cases}$