Solving Linear Systems

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System of equations are more than one equations which contain the same solution. To solve a system of equations we require the same number of equations as the number of unknown variables. An equations can consist of one or more than one unknown variables with different coefficient numbers and constant numbers.

Example 1: Solve the system of equations x - y = 15 and x + y = 25?
Solution: The given equations are x - y = 15 and x + y = 25.
Here x, y are the unknown variables. Substitute the variable x.
From one equation x = 15 + y, substituting in the other equation.
This gives 15 + y + y = 25; 15 + 2y = 25; 2y = 10; y = 5.
Now substitute y = 5 in x + y = 25; x = 20.
Hence the solution is x = 20 and y = 5.
 
Example 2: Solve the system of equations x - y = 11 and x + y = 7?
Solution: The given equations are x - y = 11 and x + y = 7.
Here x, y are the unknown variables. Substitute the variable x.
From one equation x = 11 + y, substituting in the other equation.
This gives 11 + y + y = 7; 2y + 11 = 7; 2y = 18; y = 9.
Now substitute y = 9 in x + y = 7; x = -2.
Hence the solution is x = 9 and y = 2. 

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