MAT101 Case 4 Answer Template (Case Study Sample)

MAT101 Case 4 Answer Template
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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.
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: Graphing, Substitution and Elimination
Preference/reason: Substitution, because the system is set up with the x and y variables together. It is easier for me to solve the equation even though we do it separately the are both visually there for me to remember my steps.
2. Describe a consistent system.
Answer: A Consistent System is where you can find a solution for the equations.
3. Describe an inconsistent system.
Answer: A inconsistent system is a system that offers no solution to the equation.
4. Describe a dependent system.
Answer: A dependent system When one point of the equation satisfies the other.
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=2; if x=3;
y=5-2y=5-3
y=3y=2
x

y

2

3

3

2

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

y

2

5

1

4

Answer: (1, 4)_This is a consistent independent system of linear equations
0457201657350617220001885950398145001114424-1905208597598869500188595077914500
6. 2x-2y=8
x-y=4
Calculations:
2x+2y=8
If x=2; if x=1;
y=8-4y=8-2
y=6y= 6
x

y

2

4

1

6

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

y

2

-2

1

-3

Answer: (4, 0) _ This is a consistent independent system of linear equations
157162516827516573501771650018764255867400080962585343918764251805940001657350201549000
7. 3x-y=-2
3x-y=4
Calculations:
3x-y=-2
If x=0if =1;
y=2+0y=2+3
y=2y=5
x

y

0

2

1

5

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

y

2

2

1

-1

128587519113500904875133985Answer: This is an inconsistent system of linear equations and has no solution
1666875162877500186690099060000166687540005000144780099060000
8. y=6
x=-3
Calculations:
y=6
If x=1; if x=2;
y=6y=6
y=6y=6
x

y

1

6

2

6

x=-3
If y=1; if y=3;
x=-3y=-3
x=-3y=-3
x

y

-3

1

-3

3

Answer: (3, 6) This is an inconsistent system of linear equations
904875-18382007810500083820011906250095250238125187642519050000165735019050000
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: This is an inconsistent system that has no solution.___________
10. x-y=3
x+3y=6
Calculations:
x=3+y
3+y+3y=6
3+4y=6
4y=6-3
y=0.75
x-0.75=3
x=3+0.75
x=3.75
Answer: (3.75, 0.75) This is a consistent system of linear equations _____________
11. y=-2x
4x-3y=12
Calculations:
4x-3*-2x=12
4x+6x=12
10x=12
x=1.2
1.2*4-3y=12
4.8-3y=12
4.8-12=3y
7.2=3y
y=2.4
Answer: (1.2, 2.4)_This is a consistent system of linear equations ____________
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 of linear equations ___
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)_This is a consistent system of linear equations___________
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)__ This is a consistent system of linear equations__________
15. 5x+y=2
3x+y=1
Calculations:
5x+y=2
3x+y=1
2x=1
x=0.5
5*0.5+y=2
2.5+y=2
y=2-2.5
y=-0.5
Answer: __(0.5, -0.5)_This is a consistent system of linear equations.______
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)_ This is a consistent system of linear equations.______
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
x

Y

2

Y=4-2=2

1

Y=4-1=3

y<6-3x