Q 213 Solve Systems of Equations Using... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q 213 (page 444)

Solve Systems of Equations Using Matrices
In the following exercises, solve each system of equations using a matrix.
$\{\begin{cases} - 2 x + 3 y = 3 \\ x + 3 y = 12 \end{cases}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given

A system of linear equations is given as-

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

Step 2. Concept Used

First, we will convert the given system of linear equations into its argument matrix. After that we will apply row transformation accordingly.

And we will to make zeroes in the matrix at least one through which we can find the value of one of the variable. And then we will find the value of other variable by using value of first one.

Step 3. Calculation

A system of linear equations is given as-

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

Correspond argument matrix is-

$[\begin{matrix} - 2 & 3 & 3 \\ 1 & 3 & 12 \end{matrix}]$

Apply row transformations as-

$[\begin{array}{rrc} - 2 & 3 & 3 \\ 1 & 3 & 12 \end{array}] \overset{R_{鈫�} 鈫� R_{2}}{鉄�} [\begin{array}{rrc} 1 & 3 & 12 \\ - 2 & 3 & 3 \end{array}] \overset{2 R_{1} + R_{2}}{鉄�} [\begin{array}{l} 1 & 3 & 12 \\ 0 & 9 & 27 \end{array}] \overset{\frac{1}{9} R_{2}}{鉄�} [\begin{array}{l} 1 & 3 & 12 \\ 0 & 1 & 3 \end{array}]$

Step 4. Further Calculation

Accordingly, the equations are-

$x + 3 y = 12 y = 3$

Use substitution,

$x + 3 y = 12 x + 3 (3) = 12 x + 9 = 12 x = 12 - 9 x = 3$

Step 5. Verification

Verify the equation,

$- 2 x + 3 y = 3 - 2 (3) + 3 (3) = 3 - 6 + 9 = 3 3 = 3$

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91影视

Solve Systems of Equations Using Matrices
In the following exercises, solve each system of equations using a matrix.
$\{\begin{cases} - 2 x + 3 y = 3 \\ x + 3 y = 12 \end{cases}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept Used

Step 3. Calculation

Step 4. Further Calculation

Step 5. Verification

One App. One Place for Learning.

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91影视

Solve Systems of Equations Using MatricesIn the following exercises, solve each system of equations using a matrix.-2x+3y=3x+3y=12

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept Used

Step 3. Calculation

Step 4. Further Calculation

Step 5. Verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Applied Mathematics

Pure Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Solve Systems of Equations Using Matrices
In the following exercises, solve each system of equations using a matrix.
$\{\begin{cases} - 2 x + 3 y = 3 \\ x + 3 y = 12 \end{cases}$