Question

Bring out the formulae of
"cross multiplication" method

[ Liner Equation in two variables]​

Answer 1

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Answer 2

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Let’s assume that we have to find solution for a1x + b1y + c1 = 0 (i) and a2x + b2y + c2 = 0 (ii)

Step 1: Multiply Equation (i) by b2 and Equation (ii) by b1, to get

b2a1x + b2b1y + b2c1 = 0 ---(iii)

b1a2x + b1b2 y + b1c2 = 0 ----(iv)

Step 2: Subtracting Equation (4) from (3), we get:

(b2a1 – b1a2) x + (b2b1 – b1b2) y + (b2c1– b1c2) = 0

Or (b2a1 – b1a2) x + (b2c1– b1c2) = 0

Or x = (b1c2– b2c1)/ (a1b2 – a2b1)

Step 3: Substituting this value of x in (i) or (ii), we get

y = (c1a2 – c2a1)/ (a1b2 – a2b1)

Step 4: Calculate value of a1b2 – a2b1

Step 5: if a1b2 – a2b1 ≠ 0 or a1/a2 ≠ b1/b2, then equation has definite solution.

Step 6: if a1b2 –a2b1 =0 or a1/a2 = b1/b2, then there are two possibilities

When a1/a2 = b1/b2 = c1/c2 , then there are infinitely many solutions.

When a1/a2 = b1/b2 ≠ c1/c2, then there is no solution.

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