9th Class Mathematics Linear Equations in Two Variables Important Points

         Important Points

(i) Equation for x - axis is y = 0

(ii) Equation of y - axis\[x=0\]  

(iii) Equation of a line parallel to y - axis at a distance of p from it is \[x=p\]

(iv) Equation of line parallel to x - axis at a distance of p from it is y = p

(v) Solution of pair of linear equation in two variable. Pair of linear equation is also known as a system of two simultaneous linear equations in two variable.  

The general form is

\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]

\[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]

If a pair of linear equation has at least one solution then it is said to be consistent. If a pair of linear equation has no solution then it is said to be inconsistent. In this topic we will emphasis on the solution of pair of linear equations by graphical method.  

            Graphical Method

Previously we have studied about the graph of a linear equation. Here we have a pair of linear equation which represents two lines. We know that when two lines drawn in a plane the following are the possibilities:

(i) The two lines intersect at a point.

(ii) The two lines are coincident line.

(iii) The two lines are parallel to each other.

In the above given first two conditions give the consistent solution and third one gives inconsistent solution or no solution.