Linear Equations:

Linear Equations:

Linear Equations:
Definition:A linear equation is defined as an algebraic equation in which every expression is either a stable (constant) or the product of a stable and a single variable. Linear equations can have one or more than one variables. It’s happening with great reliability in applied mathematics. A linear function is one whose diagram (graph) is a straight line.
Linear equations represent a straight line and it may be inclined or horizontal. The general format for a linear equation is as follows,

y = mx +b
where,
m = slope of the line (it is a number).

Functions of Linear Equations:
A mathematical functions is an equation which assigns a single answer to each possible question. A variable denotes an unknown value in the functions and equation.
Example for functions:

The set of all elements in functions and ordered pairs is known as domain; the set of all second elements are called range.

Example:

Functions f(x) = {(1 , 2), (3 , 4), (5 , 6), (7 , 8)}

Here Domain = { 1, 3, 5, 7 } and

Range = { 2, 4, 6, 8 }


Let us now look at few examples of Linear Equations:


Example (1)

-3/4 (16y -12) = 2/3 (18 - 9y)

1/4 (16y x -3 -12 x -3) = 1/3 (18 x 2 - 9y x 2) [Using the distributive property multiplying both the sides with their numerator]

1/4 (-48y + 36) = 1/3 (36 - 18y)

3(-48y+36) = 4(36 - 18y) [Cross multiplication ]

-144y + 108 = 144 - 72y

-144y + 72y = 144 - 108 [ Taking like terms to one side]

-72y = 36

-y = 36/72

y = -1/2 Answer


Hope you liked the example of Linear Equations,Please leave your comment if you have any doubt.