MAT101 Case 4 Answer Template (Math Problem Sample)

MAT101 Case 4 Answer Template
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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.
Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.
1. What are the 3 methods for solving systems of equations? Which one do you prefer and why?
Answer: The three methods for solving a system of linear equations are by graphing elimination, and substitution. I prefer the elimination method.
Preference/reason: The elimination method is simple and fast to use.
2. Describe a consistent system.
Answer: A consistent system is a system of equations with at least one solution. Solving consistent systems of equations using graphs will have intersecting lines or one line above another.
3. Describe an inconsistent system.
Answer: Inconsistent systems of equations have no solutions. Simply put solving them using a graph will result in parallel lines
4. Describe a dependent system.
Answer: Dependent systems of equations have infinite solutions that is graphing them will result in one line above another.
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:
107632542354500323850105219501352550299720714375785495866774471170157162578549511430001585595
Solve the following systems of equations using the graphing method.
What type of system is it? Name the solution if there is one.
5. x+y=5
-x+y=3
Calculations:
x+y=5
If x=1; and if x=2;
y=5-1y=5-2
y=4y=3
x

y

1

4

2

3

-x+y=3
If x=1; and if x=2;
y=3+1y=3+2
y=4y=5
x

y

1

4

2

5

Answer: (1, 4)_This is a consistent independent system
1114425-381018764248058150028575-38090016764005867400018764253867150
6. 2x-2y=8
x-y=4
Calculations:
2x+2y=8
If x=1; and if x=2;
y=8-2y=8-4
y=6y=4
x

y

1

6

2

4

x-y=4
If x=1; and if x=2;
y=-4+1y=-4+2
y=-3y=-2
x

y

1

-3

2

-2

Answer: ___(4, 0)_ This is a consistent independent system
156210018288000
18669005537200016478251631950090487575374518669001811020001666875201104500
7. 3x-y=-2
3x-y=4
Calculations:
3x-y=-2
If x=1; and if =0;
y=3+2y=2+0
y=5y=2
x

y

1

5

0

2

3x-y=4
If x=1; and if x=2;
y=3-4y=6-4
y=-1y=2
x

y

1

-1

2

2

Answer: This is an inconsistent system and has no solution
9144010001457325100965000166687540005000129540100018859501009650001666875160972500
8. y=6
x=-3
Calculations:
y=6
If x=1; and if =0;
y=6y=6
y=6y=6
x

y

1

6

0

6

x=-3
If y=2; and if x=5;
x=-3y=-3
x=-3y=-3
x

y

-3

2

-3

5

Answer: (3, 6) This is an inconsistent system
8667753924300086677599250500914400495300249555228600019240500166687519240500
Solve the following systems of equations using the substitution method.
What type of system is it? Name the solution if there is one.
9. x=6y+2
3x-18y=4
Calculations:
36y+2+18y=4
18y+6-18y=4
0=4-6
0=-2
Answer: _ There is no solution. _This is an inconsistent system____________
10. x-y=3
x+3y=6
Calculations:
x=3+y
3+y+3y=6
3+4y=6
4y=6-3
y=34
x-34=3
x=3+34
x=334
Answer: _(3 3/4, 3/4) This is a consistent system _____________
11. y=-2x
4x-3y=12
Calculations:
4x-3*-2x=12
4x+6x=12
10x=12
x=1210
1210*4-3y=12
4.8-3y=12
4.8-12=3y
7.2=3y
y=2.4
Answer: __(6/5, 2.4)_ This is a consistent system ____________
12. 2x-5y=15
x-7y=3
Calculations:
2x-5y=15
x=7.5-2.5y
7.5-2.5y-7y=3
7.5-4.5y=3
4.5=4.5y
y=1
2x-5=15
2x=20
x=10
Answer: __(10, 1)_ This is a consistent system ___
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. x+y=6
x-y=4
Calculations:
x+y=6
x-y=4
2x=10
x=5
5+y=6
6-5=y
y=1
Answer: ___(5, 1)____________
14. -2x+3y=5
2x-y=1
Calculations:
-2x+3y=5
2x-y= 1
2y=6
y=3
2x-3=1
2x=4
x=2
Answer: ___(2, 3)____________
15. 5x+y=2
3x+y=1
Calculations:
5x+y=2
3x+y=1
2x=1
x=12
5*12+y=2
2.5+y=2
y=2-2.5
y=-0.5
Answer: __(0.5, -0.5)_____________
16. 5x=20+y
16=3y+4x
Calculations:
5x=20+y
16=3y+4x
5x-y=20*3
4x+3y=16*1
15x-3y=60
4x+3y=16
19x=76
x=4
5*4=20+y
y=20-20
y=0
Answer: (4,0)_______________
Solve the following systems of inequalities using the graphing method.
Shade the solution set.
17. x+y>4
y+3x<6
Calculations:
x+y=4
y+3x=6
y>4-x