Chapter 6: Q18. (page 393)

Use an augmented matrix to solve each system of equations.
$\begin{matrix} y = 3 x \\ x + 2 y = 21 \end{matrix}$

Short Answer

Expert verified

The solution of the given system of equations is $(3, 9)$ .

Step by step solution

Step 1. Write the augmented matrix for the given system of equations.

The given system of equations is:

$\begin{matrix} y = 3 x \\ x + 2 y = 21 \end{matrix}$

The given system of equations can be written as:

$\begin{matrix} 3 x - y = 0 \\ x + 2 y = 21 \end{matrix}$

Place the coefficients of the equations and the constant terms into the matrix to form the augmented matrix for the given system of equations.

$[\begin{matrix} 3 & - 1 & 0 \\ 1 & 2 & 21 \end{matrix}]$

Step 2. Solve the given system of equations.

The augmented matrix is:

$[\begin{matrix} 3 & - 1 & | 0 \\ 1 & 2 & | 21 \end{matrix}]$

Interchange $R_{2}$ and $R_{1}$ .

$[\begin{matrix} 1 & 2 & 21 \\ 3 & - 1 & 0 \end{matrix}]$

Apply localid="1650979451061" $R_{2} \to R_{2} - 3 R_{1}$ ,

$[\begin{matrix} 1 & 2 & 21 \\ 0 & - 7 & - 63 \end{matrix}]$

Apply ,

$[\begin{matrix} 1 & 2 & 21 \\ 0 & 1 & 9 \end{matrix}]$

Apply $R_{1} \to R_{1} - 2 R_{2}$ ,

$[\begin{matrix} 1 & 0 & 3 \\ 0 & 1 & 9 \end{matrix}]$

Therefore, the solution of the given system of equations is $(3, 9)$ .

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Use an augmented matrix to solve each system of equations.
$\begin{matrix} y = 3 x \\ x + 2 y = 21 \end{matrix}$

Short Answer

Step by step solution

Step 1. Write the augmented matrix for the given system of equations.

Step 2. Solve the given system of equations.

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Use an augmented matrix to solve each system of equations.y=3xx+2y=21

Short Answer

Step by step solution

Step 1. Write the augmented matrix for the given system of equations.

Step 2. Solve the given system of equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use an augmented matrix to solve each system of equations.
$\begin{matrix} y = 3 x \\ x + 2 y = 21 \end{matrix}$