system of equation substitution method

System of Equation 

Free Math Education (Algebra Math) Students learn to solve systems of equations by substitution by first isolating a variable in one of the equations in the system, then substituting its value for the corresponding variable in the other equation. You can also learn to solve the equations by the method of their choice using the following rules: 

if one of the variables cancels out when the equations are added together, then use addition, and if a variable is already isolated in one of the equations, use substitution method.

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step by step solution substitution method

Substitution Method

 

Calculate value of x and y: Equations are y-x = 3 and 2(x + y) = 14


Solution:
In substitution method, we have a given equation of two variables, x and y.
First, divide in second equation by 2 in both sides.
x + y = 4 …. (1)
y – x = 3 => y = x + 3 ….(2)
Now, put the value of y in equation 1 and solve the equation for x, i.e
x + (x + 3) = 4
x + x + 3 = 4
2x = 4 –3
which gives x = 1/2.

Now, substitute x = 1/2 in any one of the given equation and find the value of y
y = 1/2 + 3
y = 7/2
Answer is : x = 1/2, y = 7/2

Linear programming problem standard form

For developing a general method of solution of a linear programming problem, we used the standard form. The basics of standard form is 

1. Non Negativity Constraints i.e. all the constraints are transformed into equations using the addition and substitution of new non negative constraints and change the equation into standard form. These new varaibles are called as slack or surplus variables and are added if <= sign in constraints and subtract if >= in the constraints.  

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Linear Programming Simplex Method

Simplex Method - Linear Programming Problem

The use of the Simplex method to solve a linear programming problem requires that the problem be converted into its standard form. The standard form of the linear Linear Programming Problem have the following characteristics.

1. All the constraints should be expressed as the adding slack variables or surplus variables or subtracting  artificial varibales.
2.  The right hand side of the each constraint should be non negative.
3.  The Objective function should be of the maximization type.

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