Finding Solution of Simultaneous Equations by Graphing

Hello students in this session we are going to talk about Finding Solution Of Simultaneous Equations By Graphing. But before discussing it you should know about linear equation, it is an algebraic expression that contains either a static term or the outcome of a static and one variable. Meaning of Simultaneous is ‘occurring at the same time’ that means we have to find Solution of Equations when they are occurring at the same time. (get detail)
The meaning of this is a pair of linear equation in two variables is said to form a system of simultaneous linear equation like
x + 2y = 3, 2x – y = 5
We can find Solution of Simultaneous Equations by Graphing with the following methods and cases they are:-
Solving Linear Equations
Method :- let the given system of linear equation be
a₁ x + b₁ y + c₁ = 0
a₂ x + b₂ y + c₂ = 0 (or try linear equations calculator)
On the same graph paper, we draw the graph of each one of the given linear equation. Each such graph is always a straight line. Let’s suppose we have two lines L₁ and L₂ that can be represented in a graph. Then many cases arise, some of them are :-
Case 1 :- When the lines L₁ and L₂ intersect at a point.
Case 2 :- When the lines L₁ and L₂ are coincident. It means they have infinitely many common points.
Case 3 :- When the lines L₁ and L₂ are parallel. It means they do not have a common point and so the system has no solution that is non-consistent. If they have at least one solution then the system is consistent.
We can make a algorithm for the above mentioned method and cases by marking them step 1, 2 to 5 so that we can easily solve Simultaneous Equations by Graphing .


In upcoming posts we will discuss about Solving by Elimination Method and Isosceles Triangle. Visit our website for information on ICSE syllabus for business studies

Substitution Method to Solving Simultaneous Equations

If two linear equations are solved at the same time then these equations are known as simultaneous. We understand the simultaneous equations by the help of some examples as
p + q = 5 and p – q = 1 are described as the simultaneous equations (more detail here).
Simultaneous equations can be solved exactly with the help of either substitution method or elimination method. Here we will use Substitution Method to Solving Simultaneous Equations. (or try linear equation calculator)
We take an example of substitution Method to Solving Simultaneous Equations as follows:
p + q = 3
2 p + 3 q = 8 (you can also try linear equation solver)
Both the equations have the sane variables p and q and both have the same solutions, so these are simultaneous equations p = 1 , q = 2 .
Substituting p = 1 and q = 2 in both the equations:
1 + 2 = 3 and 2 * 1 + 3 * 2 = 8
3 = 3 and 2 + 6 = 8 that is 8 = 8
Thus the solutions of variables p = 1 and q = 2 is correct.
For solving simultaneous Equations by the substitution method we have to follow some steps as :
step 1 : From one side of equations pick the one variable ( p )
p + q = 3
Isolate p : p = 3 – q
Step 2 : In other equation isolate the other variable :
2 p + 3 q = 8
Substitute 3 – q in place of p
2 ( 3 – q ) + 3 q = 8
This above equation has only single variable so it can solve easily .
Step 3 : For another variable q solve this equation :
2 ( 3 – q ) + 3 q = 8
Brackets are expanded as :
6 – 2 q + 3 q = 8
6 + q = 8
q = 8 – 6 = 2
q = 2
Substitute the q = 2 in equation for getting p
p = 3 – q
p = 3 – 2
Then p = 1


In upcoming posts we will discuss about Finding Solution of Simultaneous Equations by Graphing and Equilateral Triangle. Visit our website for information on CBSE board home science syllabus for class 11