Solving Systems 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 = 15 and x – y = 7?

Solution: The given equations are x + y = 15 and x – y = 7.

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

Add the two equations gives: (x+ y) + (x – y) = 15 + 7.

This gives 2x = 22; x = 22/2; x = 11.

For the y values x + y = 15; 11 + y = 15. Y = 15 – 11 = 4.

Hence the solution is x = 11 and y = 4.

Example 2: Solve by elimination the set of equations x + y = 20 and x – y = 6?

Solution: The given equations are x + y = 20 and x – y = 6.

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

Add the two equations gives: (x+ y) + (x – y) = 20 + 6.

This gives 2x = 26; x = 26/2; x = 13.

For the y values x + y = 20; 13 + y = 20. Y = 20 – 13 = 7.

Hence the solution is x = 13 and y = 7.