Question

6. Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

(i) Intersecting lines

(ii) Parallel lines

(iii) Coincident lines

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Answer 1

Answer:

Graphical Method of solving pair of linear equations in two variables

The general form for a pair of linear equations in two variables x and y is  

a1x + b1y + c1 = 0 ,

a2x + b2y + c2 = 0 ,  

Where a1, a2, b1, b2, c1, c2 are all real numbers ,a1²+ b1² ≠ 0 & a2² + b2² ≠ 0.

Condition 1: Intersecting Lines

If   a 1 / a 2 ≠  b 1 / b 2  , then the pair of linear equations has a unique solution.

Condition 2: Coincident Lines

If   a 1 / a 2 =  b 1 / b 2 =  c 1 / c 2  ,then the pair of linear equations has infinite solutions.

A pair of linear equations, which has a unique or infinite solutions are said to be a consistent pair of linear equations.

A pair of linear equations, which has  infinite many distinct common solutions are said to be a consistent pair or dependent pair of linear equations.

Condition 3: Parallel Lines

If   a 1/ a 2 =  b 1/  b 2 ≠  c 1 / c 2 , then a pair of linear equations   has no solution.

A pair of linear equations which has no solution is said to be an inconsistent pair of linear equations.

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Solution:

Given:  

2x+3y-8=0-------------------------------------(i)

i) For intersecting lines, a1 /a2 ≠ b1/b2

∴ Any line intersecting with eq i may be taken as  

3x +2y -9=0    or       3x+2y -7 =0

ii) For parallel lines ,  a1 /a2 = b1/b2 ≠ c1/ c2

∴ Any line parallel with eq i may be taken as  

6x +9y +7=0    or       2x+3y -12 =0

iii) For coincident lines, a1 /a2= b1/b2 =c1/c2

∴ Any line coincident with eq i may be taken as  

4x +6y -16=0    or       6x+9y -24 =0

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Answer 2

Answer:

I'm also fine dear :)

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1.

$a1 /a 2≠b1/b 2$

2.

$a 1 / a 2 =  b 1 / b 2 =  c 1 / c 2$

3.

$a 1/ a 2 =  b 1/  b 2 ≠  c 1 / c 2$