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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

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

1. ### Solve the linear equations:2x + 2y = 42x + 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

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

2. ### Find the unknown variables in the below equation:2x + 4y + 2z = 12x + 4y + 4z = 22x + 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