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Dependent Equation

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☼ Dependent Equation ( Parallel Lines )  : The equation of  the type  ax + by  =  c  and  kax  +  kby  =  kc   are  known as  dependent  equations  ( or parallel lines ).

Short method to solve the pair of  linear equations ( Cramer’s Rule ) :

(i) If        a1x   +  b1y  +  c1  =  0

and    a2x  +  b2 y  +  c2  =  0,

 then  Solution  is  ( x, y )  = \left (\frac{b_{1}c_{2}-b_{2}c_{1}}{a_{1}b_{2}-a_{2}b_{1}},- \frac{a_{1}c_{2}-a_{2}c_{1}}{a_{1}b_{2}-a_{2}b_{1}} \right )

(ii) If  \frac{a_{1}}{x}+\frac{b_{1}}{y}  +  c1  =  0

and  \frac{a_{2}}{x}+\frac{b_{2}}{y}  +  c2  =  0

 then  Solution  is  ( x, y )  = \left (\frac{b_{1}c_{2}-b_{2}c_{1}}{a_{1}b_{2}-a_{2}b_{1}},- \frac{a_{1}c_{2}-a_{2}c_{1}}{a_{1}b_{2}-a_{2}b_{1}} \right )

 

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