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1 a 1x + b 1 y + c 1 = 0 Intersecting unique Consistent
a 2x + b 2y + c 2 = 0 lines solution

2 a 1x + b 1 y + c 1 = 0 Coincident lines Infinitely Consistent
a 2x + b 2y + c 2 = 0 many &
solutions. Dependent

3 a 1x + b 1 y + c 1 = 0 Parallel lines no solution Inconsistent
a 2x + b 2y + c 2 = 0

Example 1: Solve the following pair of equations by cross multiplication method:

2x + 3y - 46 = 0 and 3x + 5y – 74 = 0.

Solution: Given equations are in form a 1x + b 1y + c 1 = 0 and a 2x + b 2y + c 2 = 0 and

Now, with the help of diagram we can rewrite equations

as =

=

=

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