Good evening fellow steemians today I'll be participating on "SLC S22W3//Equations and Systems of equations" and by @khursheedanwar
I must say it has really been an amazing and interesting course starting from SLC22 week 1 to week 2 and now week 3.
TASK 1 |
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Explain difference between linear and non linear systems of equations. Provide examples of each type of system of equation and describe their general forms.
- Linear Equation :A linear system of equations consists is an equations whereby each variable appears only to the first power and is not multiplied by another variable,these equations graph as straight lines, planes, or hyperplanes, depending on the number of variables.
General Forms
Where as:
a1x2+a2x2+...+and=b
X1,X2,...,Xn are variables
a1,a2....an are constants(coefficients)
b is a constants
Examples of a Linear Equation
2x+3y=6
4x-y=5
- Non Linear Equation: A linear system of equations consists of equations where each variable appears only to the first power and is not multiplied by another variable. These equations graph as straight lines, planes, or hyperplanes, depending on the number of variables.
General Forms
f1(x1,x2....xn)=0 f2(x1,x2....xn)=0
Examples of a Non Linear Equation
x²+y²=16
y-x²=4
Key Differences |
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| Features | Linear Equation | Non Linear Equation |
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| Equations | Straight line equations | curved or nonlinear equations |
| Graphs | Lines, planes or hyperplans | curved,circled , surfaces |
| Solution | Single point,no solution or infinite | May have multiple,no solution or complex |
| Example | 2x+3y=6 | x²+y²=25 |
TASKS 2 |
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Describe any one method for solving system of linear equations and share atleast one step by step algebric example
- Matrix Methods : matrix is another effective method that's used to solve Linear Equation using the inverse of a matrix .The matrix method is applicable for systems of linear equations with variables,The system is written in matrix form as:
Ax=b
Where as :
- A is the coefficient matrix
- x is the column matrix of variables
- b is the column matrix constants
The solution is given by x=A–¹b
Solving problem using Matrix Methods
TASKS 3 |
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You need for solving following system of linear equations:
(a)
x + 2y = 7
3x - 2y = 5
(b)
4x + 6y = 2
x - 2y = 3
Solution
Solving the above linear equations I'll be using the matrix method
(a). x + 2y = 7
3x - 2y = 5
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(b) 4x+6y=2
x-2y=3
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TASKS 4 |
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Scenario 1 |
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Suppose there's a company producing two products, A and B.If cost of producing x units of A and y units of B is given by system then;
2x + 3y = 130 (cost of materials)
x + 2y = 110 (cost of labor)
If company wants for producing 50 units of product A then calculate how much units of product B they may produce?
(Solve the above scenerio based questions and share step by step that how you reach to your final outcome)
Solution
Given as:
2x + 3y = 130 (cost of materials)
x + 2y = 110 (cost of labor)
The company wants to produce x = 50 units of product A. At this point, we will need to find y, the number of units of product B.
Substitute x = 50 into the equations
2(50) + 3y = 130
100 + 3y = 130
3y = 130 - 100
3y = 30
y = 10
We then substitute y to (50) in the second equation
x + 2y = 110
50 + 2y= 110
2y= 110-50
2y = 60
divide both side by coefficient of y
y=30
Final Outcome: If the company produces x = 50 , first equation y=10, second equation y=30
Scenario 2 |
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Suppose there's a bakery producing two types of cakes which are vanilla and chocolate.If cost of producing x cakes of vanilla and y cakes of chocolate is given by system then;
x + 2y = 80 (cost of ingredients)
2x + y = 70 (cost of labor)
If bakery wants for producing 30 cakes of vanilla then calculate how much cakes of chocolate can they produce?
Solution
Given as
x + 2y = 80 (cost of ingredients)
2x + y = 70 (cost of labor)
The bakery wants to produce x = 30 cakes, We will find y first which is considered as the number of chocolate cakes.
Substitute x = 30 into the equations
30 + 2y = 80
2y = 80 - 30
2y = 50
y = 25
We then subsitute x to (30)
2(30) + y = 70
2(30) + y = 70
60 + y = 70
y= 70-60
y=10
Final Outcome:x = 30 cakes of vanilla, fist equation y = 25 cakes of chocolate, second equation y=10
I'm so happy to participate on the SLC S22W3//Equations and Systems of equations by @khursheedanwar, it has always been an amazing course to learn
I'll be inviting some of my steemit friends to participate,@sahmie,@bossj23,@benton3