# Solving Systems 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 x - 5y = 30 and x + y = 6?

Solution: The given equations are x - 5y = 30 and x + y = 6.

Here x, y are the unknown variables. Substitute the variable x.

From one equation x = 30 + 5y, substituting in the other equation.

This gives 30 + 5y + y = 6; 30 + 6y = 6; 6y = -24; y = -4.

Now substitute y = -4 in x + y = 6; x = 10.

Hence the solution is x = 10 and y = -4.

Example 2: Solve by substitution the set of equations x - y = -2 and x + y = 2?

Solution: The given equations are x - y = -2 and x + y = 2.

Here x, y are the unknown variables. Substitute the variable x.

From one equation x = -2 + y, substituting in the other equation.

This gives -2+ y + y = 2; -2 + 2y = 2; 2y = 4; y = 2.

Now substitute y = 2 in x + y = 2; x = 0.

Hence the solution is x = 0 and y = 2.