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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

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

01

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:

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

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

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

02

Step 2. Solve the given system of equations.

The augmented matrix is:

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

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

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

Apply localid="1650979451061" $R_{2} 鈫� R_{2} - 3 R_{1}$ ,

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

Apply ,

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

Apply $R_{1} 鈫� R_{1} 鈭� 2 R_{2}$ ,

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

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

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Most popular questions from this chapter

Use elimination to solve each system of equations.

$\begin{array}{l} 2 x + 2 y = 4 \\ 2 x 鈭� 8 y = 鈭� 46 \end{array}$

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

$y = 2 x 鈭� 3 y = x + 4$

Use elimination to solve each system of equations.

$x + y = 9 x 鈭� y = 鈭� 3$

Use an augmented matrix to solve each system of equations.

$\begin{array}{l} 2 x + 4 y = 鈭� 16 \\ x 鈭� 2 y = 0 \end{array}$

Sean is trying to find two numbers with a sum of 14 and a difference of 4. Define two variables, write a system of equations, and solve by graphing.

See all solutions

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