Given the linear equation 2x + 3y – 12 = 0, write another linear equation in these variables, such that. geometrical representation of the pair so formed is (i) Parallel Lines (ii) Coincident Lines .
Answers
a1x + b1y + c1 = 0 ,
a2x + b2y + c2 = 0 ,
Where a1, a2, b1, b2, c1, c2 are all real numbers.
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.
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.
SOLUTION:
Given:
2x+3y-12=0.................................(i)
i) For parallel lines :
a1 /a2 = b1/b2 ≠ c1/ c2
∴ Any line parallel with eq i may be taken as
6x +9y +7=0 or 4x + 6y + 10 = 0
ii) For coincident lines:
a1 /a2= b1/b2 =c1/c2
∴ Any line coincident with eq i may be taken as
6x +9y -36=0 or 4x + 6y -24 =0
HOPE THIS WILL HELP YOU...
Step-by-step explanation:
a) Intersecting lines
Solution: For intersecting line, the linear equations should meet following condition:
a
2
a
1
=
b
2
b
1
For getting another equation to meet this criterion, multiply the coefficient of x with any number and multiply the coefficient of y with any other number. A possible equation can be as follows:
4x+9y−8=0
(b) Parallel lines
Solution: For parallel lines, the linear equations should meet following condition:
a
2
a
1
=
b
2
b
1
=
c
2
c
1
For getting another equation to meet this criterion, multiply the coefficients of x and y with the same number and multiply the constant term with any other number. A possible equation can be as follows:
4x+6y–24=0
(c) Coincident lines
Solution: For getting coincident lines, the equations should meet following condition;
a
2
a
1
=
b
2
b
1
=
c
2
c
1
For getting another equation to meet this criterion, multiply the whole equation with any number. A possible equation can be as follows:
4x+6y–16=0