Q. 20 In Problems 20鈥�25, solve each ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 20 (page 793)

In Problems 20鈥�25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} 3 x 鈭� 2 y = 1 \\ 10 x + 10 y = 5 \end{array}$

Short Answer

Expert verified

The solution in ordered pair form is $(\frac{2}{5}, \frac{1}{10})$

Step by step solution

Step 1. Given information

The given system of equations is $\{\begin{array}{r} 3 x 鈭� 2 y = 1 \\ 10 x + 10 y = 5 \end{array}$

Step 2. Solve system of equations using matrix

Write the augmented matrix of the system,

$[\begin{array}{lll} 3 & 鈭� 2 & 1 \\ 2 & 2 & 1 \end{array}]$

Perform the operation $R_{1} = \frac{R_{1}}{3}$ ,

$[\begin{array}{lll} 3 & 鈭� 2 & 1 \\ 2 & 2 & 1 \end{array}] 鈫� [\begin{array}{ccc} 1 & 鈭� \frac{2}{3} & \frac{1}{3} \\ 2 & 2 & 1 \end{array}]$

Now, perform the operation $R_{2} = R_{2} - 2 R_{1}$ ,

$[\begin{array}{ccc} 1 & 鈭� \frac{2}{3} & \frac{1}{3} \\ 2 & 2 & 1 \end{array}] 鈫� [\begin{array}{ccc} 1 & 鈭� \frac{2}{3} & \frac{1}{3} \\ 0 & \frac{10}{3} & \frac{1}{3} \end{array}]$

Now, perform the operation $R_{2} = R_{2} 路 \frac{3}{10}$ ,

$[\begin{array}{ccc} 1 & 鈭� \frac{2}{3} & \frac{1}{3} \\ 0 & \frac{10}{3} & \frac{1}{3} \end{array}] 鈫� [\begin{array}{ccc} 1 & 鈭� \frac{2}{3} & \frac{1}{3} \\ 0 & 1 & \frac{1}{10} \end{array}]$

Now, write the system of equations for this obtained augmented matrix,

$\{\begin{cases} x - \frac{2}{3} y = \frac{1}{3} \\ y = \frac{1}{10} \end{cases}$

Now,

role="math" localid="1646998275861" $x - \frac{2}{3} 路 \frac{1}{10} = \frac{1}{3} x = \frac{1}{3} + \frac{1}{15} x = \frac{2}{5}$

So, The solution in ordered pair form is $(\frac{2}{5}, \frac{1}{10})$

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91影视

In Problems 20鈥�25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} 3 x 鈭� 2 y = 1 \\ 10 x + 10 y = 5 \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve system of equations using matrix

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91影视

In Problems 20鈥�25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.3x鈭�2y=110x+10y=5

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve system of equations using matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Applied Mathematics

Decision Maths

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 20鈥�25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} 3 x 鈭� 2 y = 1 \\ 10 x + 10 y = 5 \end{array}$