Question
Sun March 08, 2015 By: Sambandan G

Show that these lines 2x+5y=1,x-3y=6,x+5y+2=0 are concurrent

Expert Reply
Prasenjit Paul
Sun March 08, 2015
I n t e r s e c t i o n space o f space t h e space l i n e s comma 2 x plus 5 y equals 1...... left parenthesis i right parenthesis x minus 3 y equals 6...... left parenthesis i i right parenthesis x plus 5 y plus 2 equals 0...... left parenthesis i i i right parenthesis S o l v i n g space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma space w e space g e t x equals 3 space a n d space y equals negative 1 I f space left parenthesis 3 comma negative 1 right parenthesis space p a s s e s space t h r o u g h space t h e space t h i r d space e q u a t i o n space x plus 5 y plus 2 equals 0 comma space t h e n space t h e space l i n e s space a r e space c o n c u r r e n t x plus 5 y plus 2 equals 0 S u b s t i t u t i n g space left parenthesis 3 comma negative 1 right parenthesis space i n space t h e space a b o v e space e q u a t i o n space 3 plus 5 left parenthesis negative 1 right parenthesis plus 2 equals 0 comma space w h i c h space s h o w s space t h e space t h i r d space e q u a t i o n space i s space s a t i s f i e d comma t h e r e f o r e space t h e space l i n e s space a r e space c o n c u r r e n t.
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