Chapter 4: Q 279 (page 459)

Explain the steps for solving a system of equations
using Cramer’s rule.

Short Answer

Expert verified

For the system of equations $\{\begin{cases} a_{1} x + b_{1} y = k_{1} \\ a_{2} x + b_{2} y = k_{2} \end{cases}$ , the solution $(x, y)$ can be determined by, $x = \frac{D_{x}}{D}$ ,

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

Where, $D = |\begin{matrix} a_{1} & b_{1} \\ a_{2} & b_{2} \end{matrix}|$

$D_{x} = |\begin{matrix} k_{1} & b_{1} \\ k_{2} & b_{2} \end{matrix}|$

$D_{y} = |\begin{matrix} a_{1} & k_{1} \\ a_{2} & k_{2} \end{matrix}|$

Step by step solution

Step 1. To explain

To explain the steps for solving the system of equations by using Cramer's rule.

Step 2. Consider the linear equation

Consider the system of linear equations,

$\{\begin{cases} - 2 x + 3 y = 3 \\ x + 3 y = 12 \end{cases}$

Step 3. Find the value of D

Evaluate the determinant $D$ by using the coefficients of variables.

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

$= - 6 - 3$

$= - 9$

The value of $D$ is $- 9$

Step 4. Find Dx

Evaluate $D_{x}$ by replacing the coefficient of $x, - 2, 1$ with the constants $3, 12$

$D_{x} = |\begin{matrix} 3 & 1 \\ 12 & 3 \end{matrix}|$

$= 9 - 12$

$= - 3$

The value of $D_{x}$ is $- 3$

Step 5. Find Dy

Evaluate $D_{y}$ by replacing the coefficient of $y, 3, 3$ by the constants $3, 12$

$D_{y} = |\begin{matrix} - 2 & 3 \\ 1 & 12 \end{matrix}|$

$= - 24 - 3$

$= - 27$

The value of $D_{y}$ is $- 27$

Step 6. Find (x,y)

Find the solution $x, y$

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

$= \frac{- 3}{- 9}$

$= \frac{1}{3}$

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

$= \frac{- 27}{- 9}$

$= 3$

The solution $(x, y)$ is $(\frac{1}{3}, 3)$

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Explain the steps for solving a system of equations
using Cramer’s rule.

Short Answer

Step by step solution

Step 1. To explain

Step 2. Consider the linear equation

Step 3. Find the value of D

Step 4. Find Dx

Step 5. Find Dy

Step 6. Find (x,y)

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Explain the steps for solving a system of equationsusing Cramer’s rule.

Short Answer

Step by step solution

Step 1. To explain

Step 2. Consider the linear equation

Step 3. Find the value of D

Step 4. Find Dx

Step 5. Find Dy

Step 6. Find (x,y)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Geometry

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Explain the steps for solving a system of equations
using Cramer’s rule.