Solving by substitution

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Substitution is a very useful method in mathematics. In the method of substitution one of the variable is substituted to find the other variables and vice versa. It helps reduce the given question or solution to a simpler form. Expressions can consist of one or more than one unknown variables with different coefficients and constant numbers.

Example 1: Solve by substitution the set of equations 3x + 2y = 12 and x + y = 6?
Solution: The given equations are 3x + 2y = 12 and x + y = 6.
Here x, y are the unknown variables. Substitute the variable x.
From one equation x = 6 - y, substituting in the other equation.
This gives 3(6-y) + 2y = 12; 18 - 3y + 2y = 12; 18 -y = 12; y = 6.
Now substitute y = 6 in x + y = 6; x = 0.
Hence the solution is x = 0 and y = 6.

 
Example 2: Solve by substitution the set of equations x - y = 0 and 2x + 5y = 7?
Solution: The given equations are x - y = 0 and 2x +5 y = 7.
Here x, y are the unknown variables. Substitute the variable x.
From one equation x = y, substituting in the other equation.
This gives 2y + 5y = 7; 7y = 7; y =1.
Now substitute y = 1 in x = y; x = 1.
Hence the solution is x = 1 and y = 1

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