two lines are given to be parallel the equation of one of the lines is 2x+3y-8=0 then find the equation for the second line
Answers
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.
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
Step-by-step explanation:
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