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Mathematics

Grade-8

Easy

Question

What is the name of lines when the following equations are drawn on a graph?
$3 x plus 4 y equals 2 6 y plus 8 y equals 4$

Intersecting lines
Parallel lines
Coincident lines
None of the above

hint Hint:

given two equations of line in the form
A1x + B1y + C1 = 0
A2x + B2y + C2 = 0
then following conditions hold
if $fraction numerator A 1 over denominator A 2 end fraction equals space fraction numerator B 1 over denominator B 2 end fraction space equals space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space c o i n c i d e n t space i f space comma space fraction numerator A 1 over denominator A 2 end fraction equals space fraction numerator B 1 over denominator B 2 end fraction space n o t space e q u a l space space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space p a r a l l e l space e l s e space i f space comma space fraction numerator A 1 over denominator A 2 end fraction space n o t space e q u a l space fraction numerator B 1 over denominator B 2 end fraction space n o t space e q u a l space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space i n t e r s e c t i n g space$

The correct answer is: Coincident lines

Given two lines
$3 x plus 4 y equals 2 6 y plus 8 y equals 4$
step 1 :
check for conditions
$fraction numerator A 1 over denominator A 2 end fraction equals space fraction numerator B 1 over denominator B 2 end fraction space equals space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space c o i n c i d e n t space i f space comma space fraction numerator A 1 over denominator A 2 end fraction equals space fraction numerator B 1 over denominator B 2 end fraction space n o t space e q u a l space space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space p a r a l l e l space e l s e space i f space comma space fraction numerator A 1 over denominator A 2 end fraction space n o t space e q u a l space fraction numerator B 1 over denominator B 2 end fraction space n o t space e q u a l space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space i n t e r s e c t i n g space$
step 2;
$3 over 6 space equals space fraction numerator 4 over denominator 8 space end fraction space equals space 2 over 4$ , condition for coincidence holds
So , Given lines are coincident

Related Questions to study

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