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This formula can be derived using elimination method. (see the video recommended
for derivation)

Sl. Pair of Equation Ratio Graphical Algebraic Consistency
No comparison Representation Interpretation
.

Step 3: Find x and y, provided or a 1b 2 – a 2b 1 ≠ 0.

Case 1 : if a 1b 2 – a 2b 1 ≠ 0 . Then the pair of linear equations has unique solution.

Case 2: if a 1b 2 – a 2b 1 = 0, i.e. , Then there are two possibilities,

(i) , Then the pair of linear equations has infinitely many solutions.

(ii) , Then the pair of linear equations has no solution.

Let us summaries the discussion

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