MAT101 Case 4 Answer Template - 4400 Words

MAT101 Case 4 Answer Template (Math Problem Sample) Content: MAT101 Case 4 Answer TemplateName: 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. The se 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

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Ca lculations: Table for x+y=5 Table for x+y=3 xy 0550xy03-30 Answer: x=1 and y=4 
Consistent independent system. 6.  QUOTE


Calculations:Table for 2x-2y=8 Table for x-y=4xy 0-440xy0-440 .Answer: Has more than one solution
Consitent dependent system.7.  QUOTE


Calculations: Table for 3x-y=-2 Table for 3x-y=4xy02-2/30xy0-44/30 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 giv es,3(6y+2) -18y=4, hence gives 18y+6-18y=4, leads to no solution.Hence no solution.It is an inconsistent systemAnswer: 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 4.5It 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=12/5It 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=10It 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=1It 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...