Given the linear equation 2x 3y 8 0

Asked by admin @ 27/08/2021 in Math viewed by 269 People

Question 6 Given the linear equation 2x + 3y − 8 = 0, write another linear equations in two variables such that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines (iii) coincident lines

Class 10 - Math - Pair of Linear Equations in Two Variables Page 50

Answered by admin @ 27/08/2021

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....

Given the linear equation 2x 3y 8 0

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