# Substitution Method Solver

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Substitution is one of the algebraic methods used to solve linear equations and other types of equations with more than one variable. In this method, one variable is written in terms of the other variable. This value of the variable is substituted into the other givenequation, thus making it an equation consisting of only a single variable and the equation is then solved for the value of the variable. Since there is substitution involved in the equations, hence it is known as the Substitution method.

Example 1:Solve using the substitution method given: x + y = 6 and x – y = 2.

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

Given x+ y = 6=>y= 6- x

Now substitute this value of ‘y’ in the second equation, x– y = 2.

This gives: x- (6- x) = 2=> x- 6 + x = 2=> 2x = 6+ 2

This gives: x= 8/2=>x = 4.

Now y = 6- x ==> y= 6– 4=> y = 2.

Example 2: Solve using the substitution method given: x + y = 11 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 = 11=> x= 11- y

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

This gives: (11 – y) – y = 7=> 11- y- y = 7=> 11- 2y= 7=>2y= 11- 7

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

Now x= 11 - y==> x= 11– 2=> x= 9.