Definition of Variable in Math

Introduction to definition of variable in math:
Variable is an alphabetic letter which is used in algebraic expression, equation, symbols. This has an unknown values and this value is a changeable one. There are two types of variable in math one is dependent variable and independent variable. There may be more than one variable in an expression.

Example Problems – Definition of Variable in Math:

Example 1 – Definition of variable in math:

Solve the given expression 5a+2b=15 for the variable a.

Solution:

The given expression is 5a+2b=15

Here the variables are a and b.

When solving for ‘a’ the answer is in terms of b and when solving for ‘b’ the answer will be in terms of ‘a’.

5a+2b=15

Subtract 2b on both sides

5a+2b-2b=15-2b

5a= 15-2b

Divide by 5 on both sides

`(5a)/5= (15-2b)/5`

`a = (15-2b)/5`

Example 2 – Definition of variable in math:

Solve the system for equations for unknown variables 2a+4b=9 and a +3b = 2.

Solution:

The given system of equations are 2a+4b=9 and a +3b = 2.

Here the unknown variables are a and b.

2a+4b=9 ------------------ (1 )

a +3b = 2 ----------------- (2 )

(1 ) ------------------ 2a+4b=9

(2 ) * 2 ------------- 2a+6b =4
(-)  (-)    (-)
--------------------
-2b = 5

Divide by -2 on both sides

`(-2b)/-2= 5/-2`

`b = -5/2.`

Now substitute the value of b in (2) to find the value of a

a +3b = 2

`a+3(-5/2)=2`

`a-15/2=2`

Add `15/2` on both sides

`a-15/2+15/2=2+15/2`

`a = 19/2`

The value of unknown variables a and b are `19/2` and `-5/2.`

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Two more Example Problems – Definition of Variable in Math:

Example 3 – Definition of variable in math:

Solve the expression 8x+2y = 10 for the variable y.

Solution:

The given expression is 8x+2y=10

Subtract 8x on both sides

8x+2y-8x=10-8x

2y=10-8x

Divide by 2 on both sides

`(2y)/2=(10-8x)/2`

`y = 5-4x.`

Example 4 – Definition of variable in math:

Find the value for a variable p from the given expression 18p+2q= 17 and q=2.

Solution:

The given expressions are 18p+2q= 17 and q=2

Here the variables are p and q.

The value of q is known so it is known variable and the p is an unknown variable.

Now plug in the value of q in the expression 18p+2q= 17 .

18p+2(2)= 17

18p+4=17

Subtract 4 on both sides

18p+4-4=17-4

18p= 13

Divide by 18 on both sides

`p = 13/18`