MAT101 Case 4 Answer Template (Math Problem Sample)

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...