# Solve by Elimination

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Elimination is a very useful method in mathematics. In the method of elimination one of the unknown variable is eliminated 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 elimination the set of equations x + y = 9 and x – y = 5?

Solution: The given equations are x + y = 9 and x – y = 5.
Here x, y are the unknown variables. Eliminate the variable y.
Add the two equations gives: (x+ y) + (x – y) = 9 + 5.
This gives 2x = 14; x = 14/2; x = 7.
For the y values x + y = 9; 7 + y = 9. Y = 9 – 7 = 2.

Hence the solution is x = 7 and y = 2.

Example 2: Solve by elimination the set of equations x + y = 1 and x – y = 11?

Solution: The given equations are x + y = 1 and x – y = 11.
Here x, y are the unknown variables. Eliminate the variable y.
Add the two equations gives: (x+ y) + (x – y) = 1 + 11.
This gives 2x = 12; x = 12/2; x = 6.
For the y values x + y = 9; 6 + y = 1. Y = 1 – 6 = -5.

Hence the solution is x = 6 and y = -5.