given a linear equation 3 x minus 5 y is equal to one form another linear equation in this variables such that the geometrical representation of linear and so formed is first intersecting lines second coincident lines third parallel lines
Answers
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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Hope this will help you....