SLC S22/W3 : Equations and Systems of Equations

Hello friends and welcome to my article in the SLC S22/W3 as organized by @khursheedanwar in this great dynamics, i would be putting in wholesome efforts to release my answers to these great tasks.

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TASK1: Explain difference between linear and non-linear system of equations. Provide examples of each type of system of equations and describe their general forms

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Linear equations: These are algebraic equations whose degree are single and easily detected in a mathematical expression. Example 4x + y = 6, where x and y are variables and 4 coefficient and 6 constant of proportionality

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^WHILE

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Non-linear equations: These are algebraic equations having two degrees or more in a mathematical expression. Example would be 2x² + y² = 4 where x and y are variables, degree 2 and 4 are constant.

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Linear Equations: These when graphically represented assume a straight line in the graph

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^WHILE

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Non-linear equations: These when graphically represented assume a parabola or curve for all to see.

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Linear equations: When mathematically represented assume the form of ax + by = 0 where x and y are variables while a, b are coefficients and 0 constant.

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^WHILE

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Non-linear equations; are in the mathematical form of ax² + by² = C where a, b Variables x and y coefficient and C is constant.

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TASK 2: Describe any method for solving system of linear equations and share at least one step by step example

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We would be making use of the Cross multiplication method in this quest

3x - 4y = 2.....eqn1
y - 2x = 7......eqn2

Equation is

^{x/b1c1-b2c1=y/c1a1-c2a2=1/b2a1-b1a2}

Where b1=4 c2=7 b2=2 c1=2 a2=1 a2=1 a1=3

After defining these parameters we immediately substitute it into the equation to simplify it.

x/28+2 = y/4+21 = 1/3-8

x/30 = y/25 = 1/5

x = -6, y = -5

We finally use a background check on the equation2 we have

-5-2(-6)=7
-5+12=7
7 = 7
This remains a linear equation

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TASK 3: You need to solve for the following linear equations x + 2y =7 3x - 2y =5 and 4x +6y =2 x -2y =3

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^{TASK 4: Suppose there's a company producing two products A and B, if cost if producing x units of A and y units of B is given by system then;}

^{2x + 3y = 130( cost of materials then)
x +2y = 110( cost of labor)}

^{If company wants for producing 50 units of products A then calculate how much unit of product B they may produce}

2x + 3y = 130.....eqn 1
x + 2y = 110......eqn 2
We form an equation 3 immediately from 2

x = 110 -2y....eqn 3

Substitute eqn 3 in eqn 1

2(110-2y) + 3y = 130
Simplify

220 - 4y + 3y = 130
Selecting like terms

-y = 130-220.
-y = -90
We divide both sides by -1
y = 90

Substituting value of y in eqn 3

x + 2(90) = 110
x + 180 = 110
x = 110-180
x = -70

b. In special occasion of 50

50 + 2y = 110
2y = 110-50

2y = 60
Divide both sides by the coefficient of y

y = 30

^{Scenario 2; Suppose there's a bakery producing two types of cake which are vanilla and chocolate, if cost of producing x cakes of vanilla and y cake of chocolate is given by system then;}

^{x + 2y = 80 ( cost of ingredients)
2x + y = 70 (cost of labor)}

We create equation 3 immediately
x = 80 - 2y

Substituting into the equation 2

2( 80-2y) + y = 70
160- 4y+ y = 70
160 - 3y = 70
-3y = -90
Divide both sides by the coefficient of y
y= 30

Substituting the value of y into equation 2
2x + 30 = 70
2x = 70-30
2x = 40

Divide both sides by the coefficient of x
x = 20

Whe we have 30 for the cakes
30 + 2y = 80
2y = 80-30
2y = 50
Divide both sides by coefficient of y

y = 25

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I have concluded my article and invite @lirvic @dove11 @mariami @nancy0 to join challenge

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