If a, b, and c are real numbers (and if a and b are not both equal to 0 simultaneously) then ax + by +c = 0 is called a linear equation in two variables. (The “two varaibles” are the x and the y.) The numbers a and b are called the coeﬃcients of the x and y respectively while c is called the constant coefficient.

A pair of linear equations in two variables can be represented, and solved, by the:

(i) graphical method (ii) algebraic method

Here we will discuss only graphical method of solving pair of linear equations.

The graph of a pair of linear equations in two variables is represented by two lines.

A pair of linear equations in two variables can be represented, and solved, by the:

(i) graphical method (ii) algebraic method

Here we will discuss only graphical method of solving pair of linear equations.

The graph of a pair of linear equations in two variables is represented by two lines.

- the lines may
**intersect**, in this case the pair of equations has a unique solution and the pair of equations is**consistent.** - the lines may be
**coincident**, in this case there are infinitely many solutions , the pair of equations is**dependent (consistent)**. - the lines may be
**parallel**, in this case the pair of equations has no solution, the pair of equations is**inconsistent**.

_{1}x+b_{1}y+c_{1}=0 and a_{2}x+b_{2}y+c_{2}=0 are two linear equations ,then the lines representing them will be- intersecting if , a
_{1}/a_{2}≠ b_{1}/b_{2} - coincident if , a
_{1}/a_{2}=b_{1}/b_{2}= c_{1}/c_{2} - parallel if , a
_{1}/a_{2}= b_{1}/b_{2}≠ c_{1}/c_{2}

Linear equations can be solved by many methods but graphical method is best for it.It illustrates more than other methods and easy to learn.

ReplyDeleteThanks a lot :) It helped me a lot :)

ReplyDelete