# Finding Solution of Simultaneous Equations by Graphing

Hello students, Previously we have discussed about irrational numbers examples and in this session we are going to know about **Finding Solution Of Simultaneous Equations By Graphing**. The method or procedure of solving a system of simultaneous linear equation of two variables by drawing their graphs is known as the graphical method. We know that the graphical representation of a linear equation in two variables is a straight line such that every point on the line represents a solution of the equation and every solution of the equation is represented by a point on the line.

Thus if there is a system of simultaneous linear equation in two variables such that the line representing the equation intersect at a point P ( a, b ). clearly the point P lies on both the lines, so its coordinates will satisfy the both the equation in the system. Thus x = a, y = b is the solution of the given system of equation.(Know more about Simultaneous Equations in broad manner, here,)

We may use the following algorithm for the **Solution of Simultaneous Equations by Graphing** for two variables :-

Algorithm :-

Step 1:- Obtain the given system of simultaneous linear equation in x and y.

let the system of simultaneous linear equation be

a_{1}x + b_{1}y = c_{1…………….1}

a_{2}x + b_{2}y = c_{2…………….2}

Step 2 :- draw the graph of the equation 1 and 2 in step 1.

then lines L_{1} and L_{2} will represents the graphs.

Step 3 :- If the lines L_{1} and L_{2}intersect at a point and ( a, b ) are the coordinates of this points, then the given system has a unique solution given by x = a, y = b, otherwise go to step 4.

Step 4 :- If the lines L_{1} and L_{2}are coincident, then the system is consistent and has infinitely many solution. In this case, every solution of one of the equation is a solution of the system, otherwise go to step 5.

Step 5 :- If the lines L_{1} and L_{2}are parallel, then the given system of equation is in- consistent that is it has no solution.

In the next session we are going to discuss **about** Two Step Linear Equation and You can visit our website for getting information about math word problem solver and cbse sample papers 2011 class ix.

## Leave a Reply