# Solving System of Equations By Elimination

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Elimination is a very useful method in mathematics. The method elimination one of the unknown variable is eliminated to find the other variables and vice versa. I 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 = -5 and x – y = 3?

Solution: The given equations are x + y = -5 and x – y = 3.

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

Add the two equations gives: (x+ y) + (x – y) = -5 + 3.

This gives 2x = -2; x = -2/2; x = -1.

For the y values x + y = -5; -1 + y = -5. Y = -5 + 1 = -4.

Hence the solution is x = -1 and y = -4.

Example 2: Solve by elimination the set of equations x + y = 8 and x – y = 3?

Solution: The given equations are x + y = 8 and x – y = 3.

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

Add the two equations gives: (x+ y) + (x – y) = 8 + 3.

This gives 2x = 11; x = 11/2; x = 5.5.

For the y values x + y = 8; 5.5 + y = 8. Y = 8 – 5.5 = 2.5.

Hence the solution is x = 5.5 and y = 2.5.