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