CHAPTER-3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
EXERCISE 3.1
QUESTION -2
On comparing the ratios a1/a2 , b1/b2 , c1/c2 find out whether the lines
representing the following pairs of linear equations intersect at a point, are
parallel or coincident:
SOLUTION:
(i) Given expressions;
Comparing these equations with a1x+b1y+c1 = 0
And a2x+b2y+c2 = 0
a1 = 5, b1 = -4, c1 = 8
a2 = 7, b2 = 6, c2 = -9
(a1/a2) = 5/7
(b1/b2) = -4/6 = -2/3
(c1/c2) = 8/-9
Since, (a1/a2) ≠ (b1/b2)
So, the pairs of equations given in the question have a unique solution and the
lines cross each other at exactly one point.
(ii) Given expressions;
Comparing these equations with a1x+b1y+c1 = 0
And a2x+b2y+c2 = 0
We get,
a1 = 9, b1 = 3, c1 = 12
a2 = 18, b2 = 6, c2 = 24
(a1/a2) = 9/18 = 1/2
(b1/b2) = 3/6 = 1/2
(c1/c2) = 12/24 = 1/2
Since (a1/a2) = (b1/b2) = (c1/c2)
So, the pairs of equations given in the question have infinite possible solutions
and the lines are coincident.
(iii) Given Expressions.
We get,
a1 = 6, b1 = -3, c1 = 10
a2 = 2, b2 = -1, c2 = 9
(a1/a2) = 6/2 = 3/1
(b1/b2) = -3/-1 = 3/1
(c1/c2) = 10/9
Since (a1/a2) = (b1/b2) ≠ (c1/c2)
So, the pairs of equations given in
Comparing these equations with a1x+b1y+c1 = 0
And a2x+b2y+c2 = 0
So, the pairs of equations given in the question are parallel to each other and the
lines never intersect each other at any point and there is no possible solution for
the given pair of equations.