Chapter 4: Q. 414 (page 485)

Solve using Cramer’s rule.
$\{\begin{cases} 3 x + y = - 3 \\ 2 x + 3 y = 6 \end{cases}$

Short Answer

Expert verified

Solution for system of linear equation is $(- \frac{15}{7}, \frac{24}{7})$

Step by step solution

Step 1. Given information

Given system of linear equation,

$\begin{array}{l} 3 x + y = - 3 \\ 2 x + 3 y = 6 \end{array}$

Step 2. Determining the solution

Variable coefficients are needed to get the determinant.

i.e.

$D = |\begin{matrix} 3 & 1 \\ 2 & 3 \end{matrix}|$

Let's evaluate the determinant.

$D = |\begin{matrix} 3 & 1 \\ 2 & 3 \end{matrix}| = (3) (3) - (1) (2) = 9 - 2 = 7$

Step 3. Finding the solution.

Let's evaluate $D_{x}$ by using the constant in place of x coefficients.

$D_{x} = |\begin{matrix} - 3 & 1 \\ 6 & 3 \end{matrix}| = (- 3) (3) - (1) (6) = - 9 - 6 = - 15$

Let's evaluate $D_{y}$ by using the constant in place of y coefficients.

$D_{y} = |\begin{matrix} 3 & - 3 \\ 2 & 6 \end{matrix}| = (3) (6) - (- 3) (2) = 18 + 6 = 24$

Step 4. Find x and y.

Put the values of $D, D_{x} a n d D_{y}$

To find x:

$x = \frac{D_{x}}{D} = - \frac{15}{7}$

To find y:

$y = \frac{D_{y}}{D} = \frac{24}{7}$

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Solve using Cramer’s rule.
$\{\begin{cases} 3 x + y = - 3 \\ 2 x + 3 y = 6 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determining the solution

Step 3. Finding the solution.

Step 4. Find x and y.

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Solve using Cramer’s rule.3x+y=-32x+3y=6

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determining the solution

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Step 4. Find x and y.

One App. One Place for Learning.

Most popular questions from this chapter

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Solve using Cramer’s rule.
$\{\begin{cases} 3 x + y = - 3 \\ 2 x + 3 y = 6 \end{cases}$