The system of linear equations 4 x − 3 y = − 1 and 3 x + 5 y = 50 and also identify the system with dependent equations and inconsistent system.

Question

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Answer 1

Question

Chapter 7, Problem 1RE

To determine

To solve: The system of linear equations 4x−3y=−1 and 3x+5y=50 and also identify the system with dependent equations and inconsistent system.

Expert Solution & Answer

Answer to Problem 1RE

The solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

Explanation of Solution

Given:

The system of linear equations is {4x−3y=−13x+5y=50.

Procedure used:

“To solve the system of linear equations by Substitution:

Step 1: Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step.)

Step 2: Substitute the expression found in step 1 into the other equation.

Step 3: Solve the equation containing one variable.

Step 4: Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the remaining variable.

Step 5: Check the obtained ordered pair by putting the corresponding value to the variables of the system of linear equations.”

Calculation:

The first equation is given below:

4x−3y=−1 (1)

The second equation is given below:

3x+5y=50 (2)

Step 1:

In equation (1), isolate the variable x as follows:

4x−3y=−14x=3y−1x=3y−14

Step 2:

Substitute 3y−14 for x in equation (2) as follows:

3(3y−14)+5y=50

Here, the variable x is eliminated.

Step 3:

Solve the equation obtained in Step 2 to find the value of y as follows:

3(3y−14)+5y=503(3y−1)+20y4=509y−3+20y=50(4)29y−3=200

Simplify the above equation as follows:

29y=200+329y=203y=20329y=7

Therefore, the value of y is 7.

Step 4:

Substitute 7 for y in equation (1) to obtain the value of x as follows:

4x−3(7)=−14x−21=−14x=−1+214x=20

Simplify the above equation as follows:

x=204x=5

Therefore, the value of x is 5.

Step 5:

Check whether the obtained solution (5,7) satisfies the given equations or not.

Substitute 5 for x and 7 for y in equation (1) to verify the obtained solution.

4(5)−3(7)=? −1 20−21=? −1 −1=−1 (True)

Substitute 5 for x and 7 for y in equation (2) to verify the obtained solution.

3(5)+5(7)=? 50 15+35 =? 50 50=50 (True)

Therefore, the obtained solution (5,7) is verified.

Thus, the solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

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Answer 2

Question

Chapter 7, Problem 1RE

To determine

To solve: The system of linear equations 4x−3y=−1 and 3x+5y=50 and also identify the system with dependent equations and inconsistent system.

Expert Solution & Answer

Answer to Problem 1RE

The solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

Explanation of Solution

Given:

The system of linear equations is {4x−3y=−13x+5y=50.

Procedure used:

“To solve the system of linear equations by Substitution:

Step 1: Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step.)

Step 2: Substitute the expression found in step 1 into the other equation.

Step 3: Solve the equation containing one variable.

Step 4: Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the remaining variable.

Step 5: Check the obtained ordered pair by putting the corresponding value to the variables of the system of linear equations.”

Calculation:

The first equation is given below:

4x−3y=−1 (1)

The second equation is given below:

3x+5y=50 (2)

Step 1:

In equation (1), isolate the variable x as follows:

4x−3y=−14x=3y−1x=3y−14

Step 2:

Substitute 3y−14 for x in equation (2) as follows:

3(3y−14)+5y=50

Here, the variable x is eliminated.

Step 3:

Solve the equation obtained in Step 2 to find the value of y as follows:

3(3y−14)+5y=503(3y−1)+20y4=509y−3+20y=50(4)29y−3=200

Simplify the above equation as follows:

29y=200+329y=203y=20329y=7

Therefore, the value of y is 7.

Step 4:

Substitute 7 for y in equation (1) to obtain the value of x as follows:

4x−3(7)=−14x−21=−14x=−1+214x=20

Simplify the above equation as follows:

x=204x=5

Therefore, the value of x is 5.

Step 5:

Check whether the obtained solution (5,7) satisfies the given equations or not.

Substitute 5 for x and 7 for y in equation (1) to verify the obtained solution.

4(5)−3(7)=? −1 20−21=? −1 −1=−1 (True)

Substitute 5 for x and 7 for y in equation (2) to verify the obtained solution.

3(5)+5(7)=? 50 15+35 =? 50 50=50 (True)

Therefore, the obtained solution (5,7) is verified.

Thus, the solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

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Answer 3

Question

Chapter 7, Problem 1RE

To determine

To solve: The system of linear equations 4x−3y=−1 and 3x+5y=50 and also identify the system with dependent equations and inconsistent system.

Expert Solution & Answer

Answer to Problem 1RE

The solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

Explanation of Solution

Given:

The system of linear equations is {4x−3y=−13x+5y=50.

Procedure used:

“To solve the system of linear equations by Substitution:

Step 1: Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step.)

Step 2: Substitute the expression found in step 1 into the other equation.

Step 3: Solve the equation containing one variable.

Step 4: Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the remaining variable.

Step 5: Check the obtained ordered pair by putting the corresponding value to the variables of the system of linear equations.”

Calculation:

The first equation is given below:

4x−3y=−1 (1)

The second equation is given below:

3x+5y=50 (2)

Step 1:

In equation (1), isolate the variable x as follows:

4x−3y=−14x=3y−1x=3y−14

Step 2:

Substitute 3y−14 for x in equation (2) as follows:

3(3y−14)+5y=50

Here, the variable x is eliminated.

Step 3:

Solve the equation obtained in Step 2 to find the value of y as follows:

3(3y−14)+5y=503(3y−1)+20y4=509y−3+20y=50(4)29y−3=200

Simplify the above equation as follows:

29y=200+329y=203y=20329y=7

Therefore, the value of y is 7.

Step 4:

Substitute 7 for y in equation (1) to obtain the value of x as follows:

4x−3(7)=−14x−21=−14x=−1+214x=20

Simplify the above equation as follows:

x=204x=5

Therefore, the value of x is 5.

Step 5:

Check whether the obtained solution (5,7) satisfies the given equations or not.

Substitute 5 for x and 7 for y in equation (1) to verify the obtained solution.

4(5)−3(7)=? −1 20−21=? −1 −1=−1 (True)

Substitute 5 for x and 7 for y in equation (2) to verify the obtained solution.

3(5)+5(7)=? 50 15+35 =? 50 50=50 (True)

Therefore, the obtained solution (5,7) is verified.

Thus, the solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

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Answer 4

Question

Chapter 7, Problem 1RE

To determine

To solve: The system of linear equations 4x−3y=−1 and 3x+5y=50 and also identify the system with dependent equations and inconsistent system.

Expert Solution & Answer

Answer to Problem 1RE

The solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

Explanation of Solution

Given:

The system of linear equations is {4x−3y=−13x+5y=50.

Procedure used:

“To solve the system of linear equations by Substitution:

Step 1: Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step.)

Step 2: Substitute the expression found in step 1 into the other equation.

Step 3: Solve the equation containing one variable.

Step 4: Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the remaining variable.

Step 5: Check the obtained ordered pair by putting the corresponding value to the variables of the system of linear equations.”

Calculation:

The first equation is given below:

4x−3y=−1 (1)

The second equation is given below:

3x+5y=50 (2)

Step 1:

In equation (1), isolate the variable x as follows:

4x−3y=−14x=3y−1x=3y−14

Step 2:

Substitute 3y−14 for x in equation (2) as follows:

3(3y−14)+5y=50

Here, the variable x is eliminated.

Step 3:

Solve the equation obtained in Step 2 to find the value of y as follows:

3(3y−14)+5y=503(3y−1)+20y4=509y−3+20y=50(4)29y−3=200

Simplify the above equation as follows:

29y=200+329y=203y=20329y=7

Therefore, the value of y is 7.

Step 4:

Substitute 7 for y in equation (1) to obtain the value of x as follows:

4x−3(7)=−14x−21=−14x=−1+214x=20

Simplify the above equation as follows:

x=204x=5

Therefore, the value of x is 5.

Step 5:

Check whether the obtained solution (5,7) satisfies the given equations or not.

Substitute 5 for x and 7 for y in equation (1) to verify the obtained solution.

4(5)−3(7)=? −1 20−21=? −1 −1=−1 (True)

Substitute 5 for x and 7 for y in equation (2) to verify the obtained solution.

3(5)+5(7)=? 50 15+35 =? 50 50=50 (True)

Therefore, the obtained solution (5,7) is verified.

Thus, the solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

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Answer 5

Chapter 7, Problem 1RE

To determine

To solve: The system of linear equations 4x−3y=−1 and 3x+5y=50 and also identify the system with dependent equations and inconsistent system.

Expert Solution & Answer

Answer to Problem 1RE

The solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

Explanation of Solution

Given:

The system of linear equations is {4x−3y=−13x+5y=50.

Procedure used:

“To solve the system of linear equations by Substitution:

Step 1: Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step.)

Step 2: Substitute the expression found in step 1 into the other equation.

Step 3: Solve the equation containing one variable.

Step 4: Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the remaining variable.

Step 5: Check the obtained ordered pair by putting the corresponding value to the variables of the system of linear equations.”

Calculation:

The first equation is given below:

4x−3y=−1 (1)

The second equation is given below:

3x+5y=50 (2)

Step 1:

In equation (1), isolate the variable x as follows:

4x−3y=−14x=3y−1x=3y−14

Step 2:

Substitute 3y−14 for x in equation (2) as follows:

3(3y−14)+5y=50

Here, the variable x is eliminated.

Step 3:

Solve the equation obtained in Step 2 to find the value of y as follows:

3(3y−14)+5y=503(3y−1)+20y4=509y−3+20y=50(4)29y−3=200

Simplify the above equation as follows:

29y=200+329y=203y=20329y=7

Therefore, the value of y is 7.

Step 4:

Substitute 7 for y in equation (1) to obtain the value of x as follows:

4x−3(7)=−14x−21=−14x=−1+214x=20

Simplify the above equation as follows:

x=204x=5

Therefore, the value of x is 5.

Step 5:

Check whether the obtained solution (5,7) satisfies the given equations or not.

Substitute 5 for x and 7 for y in equation (1) to verify the obtained solution.

4(5)−3(7)=? −1 20−21=? −1 −1=−1 (True)

Substitute 5 for x and 7 for y in equation (2) to verify the obtained solution.

3(5)+5(7)=? 50 15+35 =? 50 50=50 (True)

Therefore, the obtained solution (5,7) is verified.

Thus, the solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

Answer 6

Chapter 7, Problem 1RE

To determine

To solve: The system of linear equations 4x−3y=−1 and 3x+5y=50 and also identify the system with dependent equations and inconsistent system.

Expert Solution & Answer

Answer to Problem 1RE

The solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

Explanation of Solution

Given:

The system of linear equations is {4x−3y=−13x+5y=50.

Procedure used:

“To solve the system of linear equations by Substitution:

Step 1: Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step.)

Step 2: Substitute the expression found in step 1 into the other equation.

Step 3: Solve the equation containing one variable.

Step 4: Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the remaining variable.

Step 5: Check the obtained ordered pair by putting the corresponding value to the variables of the system of linear equations.”

Calculation:

The first equation is given below:

4x−3y=−1 (1)

The second equation is given below:

3x+5y=50 (2)

Step 1:

In equation (1), isolate the variable x as follows:

4x−3y=−14x=3y−1x=3y−14

Step 2:

Substitute 3y−14 for x in equation (2) as follows:

3(3y−14)+5y=50

Here, the variable x is eliminated.

Step 3:

Solve the equation obtained in Step 2 to find the value of y as follows:

3(3y−14)+5y=503(3y−1)+20y4=509y−3+20y=50(4)29y−3=200

Simplify the above equation as follows:

29y=200+329y=203y=20329y=7

Therefore, the value of y is 7.

Step 4:

Substitute 7 for y in equation (1) to obtain the value of x as follows:

4x−3(7)=−14x−21=−14x=−1+214x=20

Simplify the above equation as follows:

x=204x=5

Therefore, the value of x is 5.

Step 5:

Check whether the obtained solution (5,7) satisfies the given equations or not.

Substitute 5 for x and 7 for y in equation (1) to verify the obtained solution.

4(5)−3(7)=? −1 20−21=? −1 −1=−1 (True)

Substitute 5 for x and 7 for y in equation (2) to verify the obtained solution.

3(5)+5(7)=? 50 15+35 =? 50 50=50 (True)

Therefore, the obtained solution (5,7) is verified.

Thus, the solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

Answer 7

Chapter 7, Problem 1RE

To determine

To solve: The system of linear equations 4x−3y=−1 and 3x+5y=50 and also identify the system with dependent equations and inconsistent system.

Answer 8

Expert Solution & Answer

Answer to Problem 1RE

The solution set of the system of linear equations 4x−3y=−1 and 3x+5y=50 is {(5,7)}_.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given:

The system of linear equations is {4x−3y=−13x+5y=50.

Procedure used:

“To solve the system of linear equations by Substitution:

Step 1: Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step.)

Step 2: Substitute the expression found in step 1 into the other equation.

Step 3: Solve the equation containing one variable.

Step 4: Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the remaining variable.

Step 5: Check the obtained ordered pair by putting the corresponding value to the variables of the system of linear equations.”

Calculation:

The first equation is given below:

4x−3y=−1 (1)

The second equation is given below:

3x+5y=50 (2)

Step 1:

In equation (1), isolate the variable x as follows:

4x−3y=−14x=3y−1x=3y−14