explain the conditions of linear equations inteo variables
Answers
explain the conditions of linear equations into variables
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
Definition
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
The solution for such an equation is a pair of values, one for x and one for y which further makes the two sides of an equation equal.
Solution of Linear Equations in Two Variables
The solution of linear equations in two variables, ax+by = c, is a particular point in the graph, such that when x-coordinate is multiplied by a and y-coordinate is multiplied by b, then the sum of these two values will be equal to c.
Basically, for linear equation in two variables, there are infinitely many solutions.
Example
In order to find the solution of Linear equation in 2 variables, two equations should be known to us.
Consider for Example:
5x + 3y = 30
The above equation has two variables namely x and y.
Graphically this equation can be represented by substituting the variables to zero.
The value of x when y=0 is
5x + 3(0) = 30
⇒ x = 6
and the value of y when x = 0 is,
5 (0) + 3y = 30
⇒ y = 10