Math, asked by maahira17, 9 months ago

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

Answers

Answered by nikitasingh79
25

Concept :  

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

Hope this answer will help you…

 

Some more questions from this chapter :  

On comparing the ratios a1a2,b1b2 and c1c2, and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide :

(i) 5x-4y+8=0

7x+6y-9=0

(ii) 9x+3y+12=0

18x+6y+24=0

(iii) 6x-3y+10=0

2x-y+9=0

https://brainly.in/question/5484292

Solve the following systems of equations:

11x+15y+23=0

7x-2y-20=0

https://brainly.in/question/17115866

Answered by Khushibrainly
1

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 conditiओन्

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

Similar questions