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Given the linear equation 2x+3y-8=0 write …

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Given the linear equation 2x+3y-8=0 write another linear equation in two variable such that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines (iii) coincident lines

Posted by Pushkar Lohiya 1 year, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Preeti Dabral 1 year, 8 months ago

Given, linear equation is 2x + 3y - 8 = 0 ...(i)
Given: 2x + 3y - 8 = 0 ..... (i)

For intersecting lines, {tex}\frac { a _ { 1 } } { a _ { 2 } } \neq \frac { b _ { 1 } } { b _ { 2 } }{/tex}
{tex}\therefore{/tex} Any line intersecting with eq (i) may be taken as 3x + 2y - 9 = 0
or 3x + 2y - 7 = 0
For parallel lines, {tex}\frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } \neq \frac { c _ { 1 } } { c_ { 2 } }{/tex}
{tex}\therefore{/tex} Any line parallel with eq(i) may be taken as 6x + 9y + 7 = 0
or 2x +3y - 2 = 0
For coincident lines, {tex}\frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } = \frac { c _ { 1 } } { c_ { 2 } }{/tex}
{tex}\therefore{/tex} Any line coincident with eq (i) may be taken as 4x + 6y - 16 = 0
or 6x + 9y - 24 = 0

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