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# MAT101 Case 4 Answer Template (Math Problem Sample)

Instructions:

Order # 00029340 It was a math problem which i was suppose to evaluate different calculation using different methods.

source..Content:

MAT101 Case 4 Answer Template

Name:

Date:

Instructor:

Use this template to insert your answers for the assignment. Please use one of the four methods for showing your work (EE, Math Type, ALT keys, or neatly typed). Remember that your work should be clear and legible.

1. What are the 3 methods for solving systems of equations? Which one do you prefer and why?

Answer: _1.Graphing Method__2.Substitution Method_3.Elimination Method_________________________________________________

Preference/reason: _Substitution Method-Because one is able to solve one of the equations for one of the unknowns then substitute the result into the other equation hence getting the exact answers._______________________________________

2. Describe a consistent system.

Answer: _This is a system that has at least one solution. For example in a graph where two lines intercept and there is a clear solution hence called consistent system. These two lines have different slopes and different y-intercept. _____________________________________________________

3. Describe an inconsistent system.

Answer: _This is a system that has no solution. For instance two lines have same slope but different y-intercept. These lines in a graph are parallel and do not intercept hence no solution._____________________________________________________

4. Describe a dependent system.

Answer: _This is a system of two linear equation which has a one solution and this solution is exact. For example two lines in a graph that intercept and has exact point of intersection._____________________________________________________

Go to ‘insert’ and ‘shapes’. Choose the circles for the points and the lines to connect the dots. Use the arrows to represent the shading.

For example:

Solve the following systems of equations using the graphing method.

What type of system is it? Name the solution if there is one.

5. QUOTE

- QUOTE

Calculations:

Table for x+y=5 Table for –x+y=3

xy 0550

xy03-30

Answer: x=1 and y=4

Consistent independent system.

6. QUOTE

Calculations:

Table for 2x-2y=8 Table for x-y=4

xy 0-440

xy0-440

.

Answer: Has more than one solution

Consitent dependent system.

7. QUOTE

Calculations:

Table for 3x-y=-2 Table for 3x-y=4

xy02-2/30

xy0-44/30

Answer: No solutions______________________________________________

Inconsistent system.

8. QUOTE

Calculations:

Meet at an angle 90 degree.

Answer: When x=3,y=6_________________________________________________

Consistent indepandent system.

Solve the following systems of equations using the substitution method.

What type of system is it? Name the solution if there is one.

9. QUOTE

Calculations: substituting x=6y+2 in the second equation gives,

3(6y+2) -18y=4, hence gives 18y+6-18y=4, leads to no solution.

Hence no solution.

It is an inconsistent system

Answer: No solution_______________

10. QUOTE

Calculations: Making x the subject of the equation in the first equation x-y=3, will get x=3+y. Substituting x=3+y in second equation will get, (3+y) + 3y=6. Putting like terms together will get 4y=6 hence y=3/2.

To find x, return to x=3+y and substitute value of y, x=3+3/2 hence x=9/2 or 4.5

It is a consistent independent system.

Answer: x=9/2 or 4.5 and y=3/2 or 1.5_______________

11. QUOTE

Calculations: Substituting y=-2x into the second equation will get, 4x-3(-2x) =12. Putting like terms together will get 10x=12, hence x=6/5.

To find y, return to y=-2x and substitute value of x into the equation. Will get y=-2*6/5 and y=12/5

It is a consistent independent system.

Answer: _x=6/5 or 1.2 and y=12/5 or 2.4______________

12. QUOTE

Calculations: Making x to be the subject of the second equation will get, x=3+7y.

Substituting x=3+7y in the first equation will get, 2(3+7y) -5y=15.

Putting like terms together will get 9y=9 hence y=1.

To find x, return to x=3+7y and substitute value of y. x=10

It is a consistent independent system.

Answer: x=10 and y=1_______________

Solve the following systems of equations using the addition (elimination) method.

What type of system is it? Name the solution if there is one.

13. QUOTE

Calculations: Add both equations to eliminate y,

(x+y) + (x-y)=6+4 will get, 2x=10 hence x=5.

To get y replace x with 5 in the first equation,

5+y=6, y=1

It is a consistent system.

Answer: x=5 and y=1_______________

14. QUOTE

Calculations: Add both equations to eliminate x,

(-2x+3y) + (2x-y)=5+1 will get, 2y=6 hence y=3.

To get x replace y with 3 in t...

Name:

Date:

Instructor:

Use this template to insert your answers for the assignment. Please use one of the four methods for showing your work (EE, Math Type, ALT keys, or neatly typed). Remember that your work should be clear and legible.

1. What are the 3 methods for solving systems of equations? Which one do you prefer and why?

Answer: _1.Graphing Method__2.Substitution Method_3.Elimination Method_________________________________________________

Preference/reason: _Substitution Method-Because one is able to solve one of the equations for one of the unknowns then substitute the result into the other equation hence getting the exact answers._______________________________________

2. Describe a consistent system.

Answer: _This is a system that has at least one solution. For example in a graph where two lines intercept and there is a clear solution hence called consistent system. These two lines have different slopes and different y-intercept. _____________________________________________________

3. Describe an inconsistent system.

Answer: _This is a system that has no solution. For instance two lines have same slope but different y-intercept. These lines in a graph are parallel and do not intercept hence no solution._____________________________________________________

4. Describe a dependent system.

Answer: _This is a system of two linear equation which has a one solution and this solution is exact. For example two lines in a graph that intercept and has exact point of intersection._____________________________________________________

Go to ‘insert’ and ‘shapes’. Choose the circles for the points and the lines to connect the dots. Use the arrows to represent the shading.

For example:

Solve the following systems of equations using the graphing method.

What type of system is it? Name the solution if there is one.

5. QUOTE

- QUOTE

Calculations:

Table for x+y=5 Table for –x+y=3

xy 0550

xy03-30

Answer: x=1 and y=4

Consistent independent system.

6. QUOTE

Calculations:

Table for 2x-2y=8 Table for x-y=4

xy 0-440

xy0-440

.

Answer: Has more than one solution

Consitent dependent system.

7. QUOTE

Calculations:

Table for 3x-y=-2 Table for 3x-y=4

xy02-2/30

xy0-44/30

Answer: No solutions______________________________________________

Inconsistent system.

8. QUOTE

Calculations:

Meet at an angle 90 degree.

Answer: When x=3,y=6_________________________________________________

Consistent indepandent system.

Solve the following systems of equations using the substitution method.

What type of system is it? Name the solution if there is one.

9. QUOTE

Calculations: substituting x=6y+2 in the second equation gives,

3(6y+2) -18y=4, hence gives 18y+6-18y=4, leads to no solution.

Hence no solution.

It is an inconsistent system

Answer: No solution_______________

10. QUOTE

Calculations: Making x the subject of the equation in the first equation x-y=3, will get x=3+y. Substituting x=3+y in second equation will get, (3+y) + 3y=6. Putting like terms together will get 4y=6 hence y=3/2.

To find x, return to x=3+y and substitute value of y, x=3+3/2 hence x=9/2 or 4.5

It is a consistent independent system.

Answer: x=9/2 or 4.5 and y=3/2 or 1.5_______________

11. QUOTE

Calculations: Substituting y=-2x into the second equation will get, 4x-3(-2x) =12. Putting like terms together will get 10x=12, hence x=6/5.

To find y, return to y=-2x and substitute value of x into the equation. Will get y=-2*6/5 and y=12/5

It is a consistent independent system.

Answer: _x=6/5 or 1.2 and y=12/5 or 2.4______________

12. QUOTE

Calculations: Making x to be the subject of the second equation will get, x=3+7y.

Substituting x=3+7y in the first equation will get, 2(3+7y) -5y=15.

Putting like terms together will get 9y=9 hence y=1.

To find x, return to x=3+7y and substitute value of y. x=10

It is a consistent independent system.

Answer: x=10 and y=1_______________

Solve the following systems of equations using the addition (elimination) method.

What type of system is it? Name the solution if there is one.

13. QUOTE

Calculations: Add both equations to eliminate y,

(x+y) + (x-y)=6+4 will get, 2x=10 hence x=5.

To get y replace x with 5 in the first equation,

5+y=6, y=1

It is a consistent system.

Answer: x=5 and y=1_______________

14. QUOTE

Calculations: Add both equations to eliminate x,

(-2x+3y) + (2x-y)=5+1 will get, 2y=6 hence y=3.

To get x replace y with 3 in t...

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