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General Solution and Condition for Solvability

When we solve the system of equations

    a1x + b1y = c1
    a2x + b2y = c2

Either by elimination or by substitution, we get

 
, y =

Note: These values of x and y are valid only when a1b2 - a2b1 ¹ 0
 

The solution is customarily written as

     

The following diagram helps in remembering and writing the solution.

or

 
 
    

 





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