Linear Equations In Exercises 1-6, determine whether the equation is linear in the variables x and y . 2 x − y 2 = 4

Question

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Answer 1

Textbook Question

Chapter 1.CR, Problem 1CR

Linear Equations In Exercises 1-6, determine whether the equation is linear in the variables $x$ and $y .$

$2 x − y 2 = 4$

Expert Solution & Answer

To determine

Whether the equation $2x−y2=4$ is linear in the variables x and y or not.

Answer to Problem 1CR

Solution:

The equation $2x−y2=4$ is not linear in y.

Explanation of Solution

Given:

The provided equation is $2x−y2=4$ .

Definition used:

Linear Equation in n variables:

A linear equation in n variables $x1,x2,x3,...,xn$ has the form $a1x1+a2x2+a3x3+...+anxn=b$ . The coefficients $a1,a2,a3,...,an$ are real numbers, and the constant term b is a real number. The number $a1$ is the leading coefficient, and $x1$ is the leading variable.

Calculation:

Consider $2x−y2=4$ .

We know that the linear equation is of the form $a1x1+a2x2+a3x3+...+anxn=b$ where $a1,a2,a3,...,an$ are coefficients and b is the constant.

The given equation is $2x−y2=4$ .

Here we see that the power of y is 2.

Thus the given equation is not linear in y.

Final statement:

Therefore the equation $2x−y2=4$ is not linear in y.

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Name Assume there is the following simplified grade book: Homework Labs | Final Exam | Project Avery 95 98 90 100 Blake 90 96 Carlos 83 79 Dax 55 30 228 92 95 79 90 65 60 Assume that the weights used to compute the final grades are homework 0.3, labs 0.2, the final 0.35, and the project 0.15. | Write an explicit formula to compute Avery's final grade using a single inner product. Write an explicit formula to compute everyone's final grade simultane- ously using a single matrix-vector product.

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Answer 2

Textbook Question

Chapter 1.CR, Problem 1CR

Linear Equations In Exercises 1-6, determine whether the equation is linear in the variables $x$ and $y .$

$2 x − y 2 = 4$

Expert Solution & Answer

To determine

Whether the equation $2x−y2=4$ is linear in the variables x and y or not.

Answer to Problem 1CR

Solution:

The equation $2x−y2=4$ is not linear in y.

Explanation of Solution

Given:

The provided equation is $2x−y2=4$ .

Definition used:

Linear Equation in n variables:

A linear equation in n variables $x1,x2,x3,...,xn$ has the form $a1x1+a2x2+a3x3+...+anxn=b$ . The coefficients $a1,a2,a3,...,an$ are real numbers, and the constant term b is a real number. The number $a1$ is the leading coefficient, and $x1$ is the leading variable.

Calculation:

Consider $2x−y2=4$ .

We know that the linear equation is of the form $a1x1+a2x2+a3x3+...+anxn=b$ where $a1,a2,a3,...,an$ are coefficients and b is the constant.

The given equation is $2x−y2=4$ .

Here we see that the power of y is 2.

Thus the given equation is not linear in y.

Final statement:

Therefore the equation $2x−y2=4$ is not linear in y.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 1.CR, Problem 1CR

Linear Equations In Exercises 1-6, determine whether the equation is linear in the variables $x$ and $y .$

$2 x − y 2 = 4$

Expert Solution & Answer

To determine

Whether the equation $2x−y2=4$ is linear in the variables x and y or not.

Answer to Problem 1CR

Solution:

The equation $2x−y2=4$ is not linear in y.

Explanation of Solution

Given:

The provided equation is $2x−y2=4$ .

Definition used:

Linear Equation in n variables:

A linear equation in n variables $x1,x2,x3,...,xn$ has the form $a1x1+a2x2+a3x3+...+anxn=b$ . The coefficients $a1,a2,a3,...,an$ are real numbers, and the constant term b is a real number. The number $a1$ is the leading coefficient, and $x1$ is the leading variable.

Calculation:

Consider $2x−y2=4$ .

We know that the linear equation is of the form $a1x1+a2x2+a3x3+...+anxn=b$ where $a1,a2,a3,...,an$ are coefficients and b is the constant.

The given equation is $2x−y2=4$ .

Here we see that the power of y is 2.

Thus the given equation is not linear in y.

Final statement:

Therefore the equation $2x−y2=4$ is not linear in y.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 1.CR, Problem 1CR

Linear Equations In Exercises 1-6, determine whether the equation is linear in the variables $x$ and $y .$

$2 x − y 2 = 4$

Expert Solution & Answer

To determine

Whether the equation $2x−y2=4$ is linear in the variables x and y or not.

Answer to Problem 1CR

Solution:

The equation $2x−y2=4$ is not linear in y.

Explanation of Solution

Given:

The provided equation is $2x−y2=4$ .

Definition used:

Linear Equation in n variables:

A linear equation in n variables $x1,x2,x3,...,xn$ has the form $a1x1+a2x2+a3x3+...+anxn=b$ . The coefficients $a1,a2,a3,...,an$ are real numbers, and the constant term b is a real number. The number $a1$ is the leading coefficient, and $x1$ is the leading variable.

Calculation:

Consider $2x−y2=4$ .

We know that the linear equation is of the form $a1x1+a2x2+a3x3+...+anxn=b$ where $a1,a2,a3,...,an$ are coefficients and b is the constant.

The given equation is $2x−y2=4$ .

Here we see that the power of y is 2.

Thus the given equation is not linear in y.

Final statement:

Therefore the equation $2x−y2=4$ is not linear in y.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

Whether the equation $2x−y2=4$ is linear in the variables x and y or not.

Answer to Problem 1CR

Solution:

The equation $2x−y2=4$ is not linear in y.

Explanation of Solution

Given:

The provided equation is $2x−y2=4$ .

Definition used:

Linear Equation in n variables:

A linear equation in n variables $x1,x2,x3,...,xn$ has the form $a1x1+a2x2+a3x3+...+anxn=b$ . The coefficients $a1,a2,a3,...,an$ are real numbers, and the constant term b is a real number. The number $a1$ is the leading coefficient, and $x1$ is the leading variable.

Calculation:

Consider $2x−y2=4$ .

We know that the linear equation is of the form $a1x1+a2x2+a3x3+...+anxn=b$ where $a1,a2,a3,...,an$ are coefficients and b is the constant.

The given equation is $2x−y2=4$ .

Here we see that the power of y is 2.

Thus the given equation is not linear in y.

Final statement:

Therefore the equation $2x−y2=4$ is not linear in y.

Answer 8

Expert Solution & Answer

To determine

Whether the equation $2x−y2=4$ is linear in the variables x and y or not.

Answer to Problem 1CR

Solution:

The equation $2x−y2=4$ is not linear in y.

Explanation of Solution

Given:

The provided equation is $2x−y2=4$ .

Definition used:

Linear Equation in n variables:

A linear equation in n variables $x1,x2,x3,...,xn$ has the form $a1x1+a2x2+a3x3+...+anxn=b$ . The coefficients $a1,a2,a3,...,an$ are real numbers, and the constant term b is a real number. The number $a1$ is the leading coefficient, and $x1$ is the leading variable.

Calculation:

Consider $2x−y2=4$ .

We know that the linear equation is of the form $a1x1+a2x2+a3x3+...+anxn=b$ where $a1,a2,a3,...,an$ are coefficients and b is the constant.

The given equation is $2x−y2=4$ .

Here we see that the power of y is 2.

Thus the given equation is not linear in y.

Final statement:

Therefore the equation $2x−y2=4$ is not linear in y.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

Whether the equation $2x−y2=4$ is linear in the variables x and y or not.

Answer 12

Answer to Problem 1CR

Solution:

The equation $2x−y2=4$ is not linear in y.

Answer 13

Explanation of Solution

Given:

The provided equation is $2x−y2=4$ .

Definition used:

Linear Equation in n variables:

A linear equation in n variables $x1,x2,x3,...,xn$ has the form $a1x1+a2x2+a3x3+...+anxn=b$ . The coefficients $a1,a2,a3,...,an$ are real numbers, and the constant term b is a real number. The number $a1$ is the leading coefficient, and $x1$ is the leading variable.