Q. 391 In the following exercises, solv... [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. 391 (page 483)

In the following exercises, solve each system of equations using Cramer鈥檚 rule
$\{\begin{cases} x - 3 y = - 9 \\ 2 x + 5 y = 4 \end{cases}$

Short Answer

Expert verified

The ordered pair $(- 3, 2)$ is the solution for the given system of equations.

Step by step solution

Step 1. Given information

The given system of equations is:

$\{\begin{cases} x - 3 y = - 9 \\ 2 x + 5 y = 4 \end{cases}$

Step 2. Evaluating the determinant D

In determinant $D$ all the coefficients are taken.

So,

$D = |\begin{matrix} 1 & - 3 \\ 2 & 5 \end{matrix}|$

$D = 1 脳 5 - (- 3 脳 2) D = 5 + 6 D = 11$

Step 3. Evaluating the determinant Dx

In determinant $D_{x}$ , we take the constants in place of coefficients of $x$

So.

$D_{x} = |\begin{matrix} - 9 & - 3 \\ 4 & 5 \end{matrix}| D_{x} = - 9 脳 5 - (- 3 脳 4) D_{x} = - 45 + 12 D_{x} = - 33$

Step 4. Evaluating the determinant Dy

In the determinant $D_{y}$ , we take the constant in place of coefficients of $y$

So,

$D_{y} = |\begin{matrix} 1 & - 9 \\ 2 & 4 \end{matrix}| D_{y} = 1 脳 4 - (- 9 脳 2) D_{y} = 4 + 18 D_{y} = 22$

Step 5. Finding x and y

For $x$

$x = \frac{D_{x}}{D} x = \frac{- 33}{11} x = - 3$

For $y$

$y = \frac{D_{y}}{D} y = \frac{22}{11} y = 2$

Step 6. Writing solution in ordered pair

The solution of the system in ordered pair is $(- 3, 2)$

Step 7. Check the solution for x − 3y = −9

Substituting $x = - 3 y = 2$ in the equation, we get:

$x 鈭� 3 y = 鈭� 9 - 3 - 3 (2) = - 9 - 3 - 6 = - 9 - 9 = - 9$

This is true

Step 8. Check the solution for 2x + 5y = 4

Substituting $x = - 3 y = 2$ in the equation, we get:

$2 x + 5 y = 4 2 (- 3) + 5 (2) = 4 - 6 + 10 = 4 4 = 4$

This is also true.

Thus, the ordered pair $(- 3, 2)$ is the solution.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In the following exercises, solve each system of equations using Cramer鈥檚 rule
$\{\begin{cases} x - 3 y = - 9 \\ 2 x + 5 y = 4 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating the determinant D

Step 3. Evaluating the determinant Dx

Step 4. Evaluating the determinant Dy

Step 5. Finding x and y

Step 6. Writing solution in ordered pair

Step 7. Check the solution for x − 3y = −9

Step 8. Check the solution for 2x + 5y = 4

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Applied Mathematics

Pure Maths

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

In the following exercises, solve each system of equations using Cramer鈥檚 rulex-3y=-92x+5y=4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating the determinant D

Step 3. Evaluating the determinant Dx

Step 4. Evaluating the determinant Dy

Step 5. Finding x and y

Step 6. Writing solution in ordered pair

Step 7. Check the solution for x − 3y = −9

Step 8. Check the solution for 2x + 5y = 4

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Applied Mathematics

Pure Maths

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system of equations using Cramer鈥檚 rule
$\{\begin{cases} x - 3 y = - 9 \\ 2 x + 5 y = 4 \end{cases}$