On comparing
the ratio a1/a2 ,b1/b2,c1/c2 .Find out whether the following pair of linear equations are consistent or inconsistent
(4/3) x + 2y-8=0
2x + 3y - 12 = 0
Answers
Answered by
1
Answer:
The above equation is inconsistent
Answered by
30
HERE IS YOUR ANSWER MATE.....;
(i) Given : 3x + 2y = 5 or 3x + 2y – 5 = 0 :-
and 2x – 3y = 7 or 2x – 3y – 7 = 0
Comparing the above equations with a1x + b1y + c1=0
And a2x + b2y + c2 = 0
We get,
a1 = 3, b1 = 2, c1 = -5
a2 = 2, b2 = -3, c2 = -7
a1/a2 = 3/2, b1/b2 = 2/-3, c1/c2 = -5/-7 = 5/7
Since, a1/a2≠b1/b2 the lines intersect each other at a point and have only one possible solution.
Hence, the equations are consistent.
(ii) Given 2x – 3y = 8 and 4x – 6y = 9 :-
Therefore,
a1 = 2, b1 = -3, c1 = -8
a2 = 4, b2 = -6, c2 = -9
a1/a2 = 2/4 = 1/2, b1/b2 = -3/-6 = 1/2, c1/c2 = -8/-9 = 8/9
Since, a1/a2=b1/b2≠c1/c2
Therefore, the lines are parallel to each other and they have no possible solution. Hence, the equations are inconsistent.
Similar questions