Substitution Method

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A linear equation can be written in terms of a single variable, two variables or more than two variables. In order to solve a linear equation with two variables, we need another equation with two variables as well. Substitution method is one of the popular algebraic methods of solving linear equations with more than one variable. In this method, one variable is written in terms of the other and is substituted back into the equation to get the values of the unknown variables.

Example 1:  Solve using the substitution method given: x + y = 3 and x – y = 7.

In Substitution method, either ‘x’ or ‘y’ can be chosen to be written in terms of the other.

Given x+ y = 3==> y= 3 – x

Now substitute this value of ‘y’ in the second equation, x– y = 7.

This gives: x– (3 – x) = 7==>x– 3 + x = 7==> 2x= 7+ 3.

This gives: x= 10/2==> x = 5.

Now y = 3- x ==> y= 3– 5==> y = -2.
 
Example 2: Solve using the substitution method given: x + y = 5 and x – y = 1.

In Substitution method, either ‘x’ or ‘y’ can be chosen to be written in terms of the other.

Given x+ y = 5==> x= 5 – y

Now substitute this value of ‘x’ in the second equation, x– y = 1.

This gives: (5- y) – y = 1==> 5 – y – y = 1==> 5- 2y= 1==> 2y= 5- 1

This gives: y= 4/2==>y= 2.

Now x= 5- y==> x= 5– 2==>x= 3.
 

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