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Variable Calculator
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Variables are the lower letter alphabets which contain a constant value which can be vary as per the condition.
Example: The bus speed is given by a variable x(say)
Algebraic Equation: x + y = 12
In the above equation x and y are the variables and 12 is the constant.

In a 2 linear systems of equations, there are 2 unknown variables and we need to find those 2 unknown variables. Similarly in a 3 linear systems of linear equations, there are 3 unknown variables and we need to find those 3 unknown variables.

Variable Calculator
is used to solve the liner system of equations. It calculates the value for the unknown variables.
 

Steps for Variable Calculator

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Step 1 :  

Observe the given equations, check for 2 x 2 or 3 x 3.



Step 2 :  

If the given equations are 2 x 2, then solve it by:


$\Rightarrow$ Find the easiest equation out them and solve it for x or y.


$\Rightarrow$ Substitute that equation into other equation and solve it for x or y. After getting the either of the variable, just substitute in either of the equation and solve for the variable.



Step 3 :  

If the given equations are 3 x 3, then solve it by:


$\Rightarrow$ Solve equation 1 and equation 2 by elimination method or substitution method and name it as equation 4.


$\Rightarrow$ Solve equation 2 and equation 3 by elimination method or  substitution method and name it as equation 5.


$\Rightarrow$ Now solve equation 4 and equation 5 which gives the value of two variables. Substitute the value of those two variables in any of the equation and solve it further to obtain the value of third variable. 


 



Problems on Variable Calculator

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  1. Solve the linear equations:

    2x + 2y = 4

    2x + 1y = 2


    Step 1 :  

    Given equations:


    2x + 2y = 4 $\Rightarrow$ 2x = 4 - 2y $\Rightarrow$ x = 2 - y



    Step 2 :  

    Now consider the second equation: 2x + 1y = 2


    substitute x = 2 - y in the above equation


    2x + 1y = 2


    2(2 - y) + 1y = 2


    4 - 2y + y = 2


    -y = 2 - 4 $\Rightarrow$ y = 2



    Step 3 :  

    substitute y = 2 in the either of the equation


    2x + 1y = 2 $\Rightarrow$ 2x + 1(2) = 2 $\Rightarrow$ 2x = 0 $\Rightarrow$ x = 0



    Answer  :  

    So, (x, y) = (0, 2)



  2. Find the unknown variables in the below equation:

    2x + 4y + 2z = 1

    2x + 4y + 4z = 2

    2x + 2y + 4z = 6


    Step 1 :  

    Given linear equations:


    2x + 4y + 2z = 1---equation(1)


    2x + 4y + 4z = 2---equation(2)


    2x + 2y + 4z = 6---equation(3)



    Step 2 :  

    Solve equation(1) and equation(2)


    2x + 4y + 2z = 1


    2x + 4y + 4z = 2   


                   -2z = -1


    z = 0.5


    Solve equation(2) and equation(3)


    2x + 4y + 4z = 2


    2x + 2y + 4z = 6   


            2y + 0 = -3 


    y = -2


     



    Step 3 :  

    substitute z =0.5 and y = -2 in either of the equations


    2x + 4y + 2z = 1


    $\Rightarrow$ 2x + 4(-2) + 2(0.5) = 1


    $\Rightarrow$ 2x -8 + 1 = 1


    $\Rightarrow$ 2x = 1 + 7 = 8


    $\Rightarrow$ x = 4



    Answer  :  

    So, (x, y, z) = (4, -2, 0.5)



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