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