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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: Q20. (page 393)

Use an augmented matrix to solve each system of equations.
$x + y = 15 x 鈭� y = 9$

Short Answer

Expert verified

The solution of the given system of equations is $(12, 3)$ .

Step by step solution

01

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

The given system of equations is:

$x + y = 15 x 鈭� y = 9$

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

$[\begin{matrix} 1 & 1 & 15 \\ 1 & 鈭� 1 & 9 \end{matrix}]$

02

Step 2. Solve the given system of equations.

The augmented matrix is:

$[\begin{matrix} 1 & 1 & 15 \\ 1 & 鈭� 1 & 9 \end{matrix}]$

Apply $R_{2} 鈫� R_{2} 鈭� R_{1}$ ,

$[\begin{matrix} 1 & 1 & 15 \\ 0 & 鈭� 2 & 鈭� 6 \end{matrix}]$

Apply $R_{2} 鈫� \frac{鈭� 1}{2} R_{2}$ ,

$[\begin{matrix} 1 & 1 & 15 \\ 0 & 1 & 3 \end{matrix}]$

Apply $R_{1} 鈫� R_{1} 鈭� R_{2}$ ,

$[\begin{matrix} 1 & 0 & 12 \\ 0 & 1 & 3 \end{matrix}]$

Therefore, the solution of the given system of equations is $(12, 3)$ .

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Most popular questions from this chapter

Use elimination to solve each system of equations.

$\begin{array}{l} 8 x 鈭� 5 y = 18 \\ 6 x + 6 y = 鈭� 6 \end{array}$

Solve each equation or formula for the variable specified.

$2 x + 4 y = 12$ , for x

Perform the indicated matrix operation.

$[\begin{matrix} 5 & 鈭� 8 & 4 \\ 鈭� 6 & 2 & 鈭� 9 \end{matrix}] 鈭� [\begin{matrix} 6 & 鈭� 4 & 鈭� 3 \\ 8 & 2 & 1 \end{matrix}]$

Use substitution to solve each system of equations.

$\begin{array}{l} y = 5 x 鈭� 3 \\ x + 2 y = 27 \end{array}$

Use elimination to solve each system of equations.

$\begin{array}{l} 鈭� 9 x + 3 y = 鈭� 3 \\ 3 x 鈭� 2 y = 鈭� 4 \end{array}$

See all solutions

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